Slope of Tangent to Cycloid

Theorem
Let $C$ be a cycloid generated by the equations:
 * $x = a \paren {\theta - \sin \theta}$
 * $y = a \paren {1 - \cos \theta}$

The slope of the tangent to $C$ at the point $\tuple {x, y}$ is given by:
 * $\dfrac {\d y} {\d x} = \cot \dfrac \theta 2$