0
    \begin{align}
        \sin^2 \theta_{12} &= {\bigg[-2 (\cos (\sigma) \sin (2 \phi) + 1)\bigg]}\bigg/
        {\bigg[\sqrt{3} \sin (2 \phi) \sin (2 \phi') \cos (\sigma - \sigma') - 4 \cos (\sigma) \sin (\phi) \cos (\phi) \sin^2(\phi') + \sin^2(\phi) 
        \left(-\sqrt{3} \cos (\sigma') \sin (2 \phi') + \cos (2 \phi') + 2\right) + 4 \cos^2(\phi) \sin^2(\phi') - 6\bigg]} \nonumber\\
        \sin^2 \theta_{23} &= \frac{\bigg[-\sqrt{3} \cos (\sigma') \sin (2 \phi') - \cos (2 \phi') - 2\bigg]}
        {\bigg[\sqrt{3} \sin (2 \phi) \sin (2 \phi') \cos (\sigma - \sigma') - 4 \cos (\sigma) \sin (\phi) \cos (\phi) \sin^2(\phi') + \sin^2(\phi) 
        \left(-\sqrt{3} \cos (\sigma') \sin (2 \phi') + \cos (2 \phi') + 2\right) + 4 \cos^2(\phi) \sin^2(\phi') - 6\bigg]} \nonumber\\
        \sin^2 \theta_{13} &= \frac{1}{6} \bigg[\sqrt{3} \sin (2 \phi) \sin (2 \phi') \cos (\sigma - \sigma) - 4 \cos (\sigma) \sin (\phi) \cos (\phi) \sin^2(\phi') + \sin^2(\phi) 
        \left(-\sqrt{3} \cos (\sigma') \sin (2 \phi') + \cos (2 \phi') + 2\right) + 4 \cos^2(\phi) \sin^2(\phi')\bigg] \nonumber\\
    \end{align}
1
  • 3
    Welcome. // Please add the missing lines, so your code will compile when we copy it. Also often a screenshot helps to better understand your problem. Thank you
    – MS-SPO
    Commented Jul 9 at 11:22

3 Answers 3

5

This is really more of a math problem than a TeX problem. You have really long expressions that you're trying to fit into a page: you need to figure out how they'll fit and then tell TeX what to do. Since you have a large expression that recurs several times, I would split that out as its own thing:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align}
        \sin^2 \theta_{12} &= \frac{-2 (\cos (\sigma) \sin (2 \phi) + 1)}
        {D - 6} \nonumber\\
        \sin^2 \theta_{23} &= \frac{-\sqrt{3} \cos (\sigma') \sin (2 \phi') - \cos (2 \phi') - 2}
        {D - 6} \nonumber\\
        \sin^2 \theta_{13} &= \frac{D}{6}
    \end{align}
where
\begin{multline*}
D=
\sqrt{3} \sin (2 \phi) \sin (2 \phi') \cos (\sigma - \sigma) - 4 \cos (\sigma) \sin (\phi) \cos (\phi) \sin^2(\phi') \\
+ \sin^2(\phi) \bigl(-\sqrt{3} \cos (\sigma') \sin (2 \phi') + \cos (2 \phi') + 2\bigr) + 4 \cos^2(\phi) \sin^2(\phi')
\end{multline*}

\end{document}

code output

A few other quick notes:

  • \left and \right are good for quick editing, but you should switch to manual sizing once you're done
  • Use \bigl( instead of \big( (and all the other variations of that statement)
  • Ending with \nonumber\\ causes the equation number to be too low
2
  • Does the OP want to number any of the first three equations?
    – Mico
    Commented Jul 9 at 17:39
  • 1
    @Mico That is definitely unclear. Making the minimal changes to OP's code to get it to compile does result in a single equation number, so I left it in there.
    – Teepeemm
    Commented Jul 9 at 17:45
2

Here's a variation on @Teepeemm's fine answer. I mainly suggest (a) using inline-fraction notation in the first three rows to further compactify the expressions and (b) getting rid of all unnecessary parentheses. And, I'd nest an align* environment and a multlined environment inside a gather* environment, both to get rid of all three \nonumber directives and to further "snug up" the overall appearance of the equations.

enter image description here

\documentclass{article} % or some other suitable document class
\usepackage{mathtools}  % for '\shortintertext' macro

\begin{document}

\hrule % just to illustrate width of text block

\begin{gather*}
\begin{align*}
\sin^2\theta_{12} &= -2 (\cos\sigma \sin2\phi + 1) / D \\
\sin^2\theta_{23} &= (-\sqrt{3} \cos\sigma' \sin2\phi' - \cos2\phi' - 2) / D \\
\sin^2\theta_{13} &= D/6 + 1 
\end{align*}
\shortintertext{where}
\begin{multlined}
D=\sqrt{3} \sin2\phi \sin2\phi' \cos (\sigma - \sigma') 
   - 4 \cos\sigma \sin\phi \cos\phi \sin^2\phi' \\
   + \sin^2\phi (-\sqrt{3} \cos\sigma' \sin2\phi' 
   + \cos2\phi' + 2) + 4 \cos^2\phi \sin^2\phi' - 6 \,.
\end{multlined}
\end{gather*}

\end{document}
2

Another possibility by use of the \splitfrac and multlined of mathtools package:

\documentclass{article}
\usepackage{geometry}
\usepackage{mathtools}

\begin{document}
   \begin{align}
\sin^2 \theta_{12} 
    & = \frac{{-2 (\cos (\sigma) \sin (2 \phi) + 1)}}
             {\bigg[\splitfrac{
             \sqrt{3} \sin (2 \phi) \sin (2 \phi') \cos (\sigma - \sigma') 
                - 4 \cos (\sigma) \sin (\phi) \cos (\phi) \sin^2(\phi') 
                        }{
                + \sin^2(\phi) \left(-\sqrt{3} \cos (\sigma') \sin (2 \phi') + \cos (2 \phi') + 2\right) 
                + 4 \cos^2(\phi) \sin^2(\phi') - 6}\bigg]
             }                      \nonumber   \\[\jot]
\sin^2 \theta_{23} 
    & = \frac{-\sqrt{3} \cos (\sigma') \sin (2 \phi') - \cos (2 \phi') - 2}
             {\bigg[\splitfrac{
             \sqrt{3} \sin (2 \phi) \sin (2 \phi') \cos (\sigma - \sigma') 
                - 4 \cos (\sigma) \sin (\phi) \cos (\phi) \sin^2(\phi') 
                        }{
                + \sin^2(\phi) \left(-\sqrt{3} \cos (\sigma') \sin (2 \phi') + \cos (2 \phi') + 2\right) 
                + 4 \cos^2(\phi) \sin^2(\phi') - 6}\bigg]
             }                      \nonumber   \\[\jot]
\sin^2 \theta_{13} 
    & = \frac{1}{6} \left[
        \begin{multlined}
        \sqrt{3} \sin (2 \phi) \sin (2 \phi') \cos (\sigma - \sigma) - 4 \cos (\sigma) \sin (\phi) \cos (\phi) \sin^2(\phi')        \\
            + \sin^2(\phi) 
        \left(-\sqrt{3} \cos (\sigma') \sin (2 \phi') + \cos (2 \phi') + 2\right) + 4 \cos^2(\phi) \sin^2(\phi')
        \end{multlined}
                    \right]
    \end{align}
   \end{document} 

enter image description here

Edit: Considered @Mico comment.

2
  • Do you need the tall square brackets in the numerators of the first two rows?
    – Mico
    Commented Jul 9 at 17:27
  • 1
    @Mico, actually no. I will remove them ASAP
    – Zarko
    Commented Jul 9 at 20:03

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