# How do I remove extra spacing on a new page following an align*?

I have the following code:

%...
\begin{proof}
Let $P=(x_P, y_P, z_P)$ be a fixed point on the plane, $R$ a fixed length, and $X=(x,y,z)$ a
variable point such that $XP=R$. As $X$ varies, it is obvious that it does so along a circle.
Obviously, we have the displacement vector $\vv{XP}=(x_P - x, y_P - y, z_P - z)$.
Using \ref{distance}, it follows that

\begin{align*}
& XP^2 = - \sum_{cyc} a^2 (y_P - y)(z_P - z) \\
\Leftrightarrow & R^2 = -\sum_{cyc} y_P z_P a^2 + \sum_{cyc} y_P a^2 z
+ \sum_{cyc} z_P a^2 y - \sum_{cyc} a^2 yz \\
%...


And the following output is produced:

You may notice that there is more spacing than the default 1 inch margin at the top of the new page. It also happens that if I remove the extra space before the beginning of the align* sequence, the last sentence of the last page appears in the next page, filling the extra space. How do I remove this extra space?

• never leave a blank line before a displayed equation (whether \[ or equation or align etc), it will always make bad spacing. – David Carlisle Jan 25 '16 at 20:56
• When that blank line is removed, the page breaking is controlled by two parameters: \predisplaypenalty (usually 10000) for a break before the display and \displaywidowpenalty (usually 50) for a break before the last line above the display. Since 10000 is effectively infinite, the previous line stays with the display. You could temporarily set \predisplaypenalty=0 to allow a page break before the display. – Dan Jan 25 '16 at 22:44

I did the best I could with no MWE.

\documentclass{article}
\usepackage{mathtools}
\usepackage{showframe}
\begin{document}
\rule{1pt}{41\baselineskip}

Let $P=(x_P, y_P, z_P)$ be a fixed point on the plane, $R$ a fixed length, and $X=(x,y,z)$ a
variable point such that $XP=R$. As $X$ varies, it is obvious that it does so along a circle.
Obviously, we have the displacement vector $\vec{XP}=(x_P - x, y_P - y, z_P - z)$.
Using \ref{distance}, it follows that
\pagebreak[3]
\begin{align*}
& XP^2 = - \sum_{cyc} a^2 (y_P - y)(z_P - z) \\
\Leftrightarrow & R^2 = -\sum_{cyc} y_P z_P a^2 + \sum_{cyc} y_P a^2 z
+ \sum_{cyc} z_P a^2 y - \sum_{cyc} a^2 yz \\
\end{align*}

\end{document}