Let $R(x, \theta)$ denote anti-clockwise rotation of the Euclidean plane $\mathbb{R}^{2}$ through an angle $\theta$ about a point $x$.

Show that $R(x, \theta)$ is a composite of two reflexions.

Assume $\theta, \phi \in(0, \pi)$. Show that the composite $R(y, \phi) \cdot R(x, \theta)$ is also a rotation $R(z, \psi)$. Find $z$ and $\psi$.