just enabled using drush.
$
h \leq \frac{1}{2} |\zeta - z| [ |\zeta - z - h| \geq \frac{1}{2} |\zeta - z|]
$
implies
$
\left| \frac{1}{\zeta - z - h} - \frac{1}{\zeta - z} \right|
= \left|
\frac{(\zeta - z) - (\zeta - z - h)}{(\zeta - z - h)(\zeta - z)}
\right| \ =
\left| \frac{h}{(\zeta - z - h)(\zeta - z)} \right| \
\leq \frac{2 |h|}{|\zeta - z|^2}.
$
$
\cos 2\theta = \cos^2 \theta - \sin^2 \theta
= 2 \cos^2 \theta - 1.$