How do I Calculate the rotation corresponding to the following Unitary Matrix (Quantum Math)

Question

\begin{pmatrix}e^{i\pi }\cos\theta &-e^{-i\pi \:}\sin\theta \\ -\sin\theta \:&-\cos\theta \:\end{pmatrix}

Answer 1

We have $\begin{pmatrix}e^{i\pi}\cos\theta&-e^{-i\pi}\sin\theta \\-\sin\theta&-\cos\theta \end{pmatrix}=\begin{pmatrix}-\cos\theta &\sin\theta \\-\sin\theta &-\cos\theta \end{pmatrix}=(-1)\begin{pmatrix}\cos\theta &-\sin\theta \\\sin\theta&\cos\theta \end{pmatrix}=\begin{pmatrix}\cos (\theta +\pi)&-\sin (\theta+\pi)\\\sin (\theta+\pi)&\cos (\theta+\pi)\end{pmatrix}$.

This is a rotation by $\theta +\pi$.