What is the cardinality of the set of $\theta \in[0,2 \pi)$ such that the linear map $\mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ given by the matrix:
\[
\left(\begin{array}{cc}
\cos \theta & -\sin \theta \\
\sin \theta & \cos \theta
\end{array}\right)
\]
has an eigenvector in $\mathbb{R}^{2}$ ?
- $1$
- $2$
- $4$
- $\infty$
