如何删除 align* 后新页面上的多余空格？

Question

我有以下代码：

%...
\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 \\
%...

并产生以下输出：

您可能会注意到，新页面顶部的间距比默认的 1 英寸边距要大。此外，如果我删除 align* 序列开始前的额外空间，最后一页的最后一句话就会出现在下一页中，填补额外的空间。我该如何删除这个额外的空间？

Answer 1

在没有 MWE 的情况下，我已经尽力了。

\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}