Slope of Tangent to Cycloid

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

The tangent to $C$ at the point $\left({x, y}\right)$ is given by:
 * $\dfrac {\mathrm d y} {\mathrm d x} = \cot \dfrac \theta 2$