Isometry/R^4/Two axes reflections/Exercise

The matrix

$\left(\begin{array}{cccc}\cos \alpha & \sin \alpha & 0& 0\\ \sin \alpha & -\cos \alpha & 0& 0\\ 0& 0& \cos \beta & \sin \beta \\ 0& 0& \sin \beta & -\cos \beta \end{array}\right)$

defines a linear mapping $\phi :{ℝ}^4\to {ℝ}^4$ ($\alpha ,\beta \in [0,\pi [$). Determine the eigenvalues of $\phi$ and their algebraic and geometric multiplicities.

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