Reducible representation of $SO(2)$ on $\mathbb R^3$

Question

A representation of $SO(2)$ on $\mathbb R^3$ is the the map $$\begin{bmatrix}\cos\theta & \sin\theta\\ -\sin\theta & \cos\theta\end{bmatrix} \rightarrow\begin{bmatrix}\cos\theta & \sin\theta&0\\ -\sin\theta & \cos\theta&0\\0&0&1\end{bmatrix}$$ This representation is reducible because when it acts on a plane of $\mathbb R^3$ it leaves the vectors on the plane. My question is, how can I decompose this representation in a composition of irreducible representations?