Linear Transformations · Challenge problem

The matrix $A = \dfrac13\begin{pmatrix}2 & -1 & 2\\2 & 2 & -1\\-1 & 2 & 2\end{pmatrix}$ is the matrix of a rotation of $\mathbb{R}^3$ about some axis through the origin. Through what angle, in degrees between $0$ and $180$, does it rotate?