I would like to align the first "+" in the third and fourth lines of the following code. In the third line, I have "= 3 + [a mess]" and in the fourth line, I have "+ [another mess]" - I don't have the "3" in the fourth line. I used the \hphantom command to account for the horizontal space of the "= 3" in the third line, but there is a small space, the space that surrounds either side of a binary operator - in this case a plus sign - that needs to be inserted. (I am using 10pt font in amsart.) Here is the code :
\begin{align*}
&\vert xy + xz + yz \vert^{2} \\
&\qquad = [\cos(a + b) + \cos(a + c) + \cos(b + c)]^{2}
+ [\sin(a + b) + \sin(a + c) + \sin(b + c)]^{2} \\
&\qquad = 3 + [2\cos(a + b)\cos(a + c)
+ 2\cos(a + b)\cos(b + c)
+ 2\cos(a + c)\cos(b + c)] \\
&\qquad \hphantom{= 3} + [2\sin(a + b)\sin(a + c)
+ 2\sin(a + b)\sin(b + c)
+ 2\sin(a + c)\sin(b + c)] .
\end{align*}
I tried using a \phantom
command with a \mathbin{+}
command, but that added the horizontal space of the plus sign to the fourth line. I tried to put another align environment within the given align environment.
\hphantom{{}= 3}