Isometry/R^4/Two axes reflections/Exercise

The matrix

${\begin{pmatrix}\cos \alpha &\sin \alpha &0&0\\\sin \alpha &-\cos \alpha &0&0\\0&0&\cos \beta &\sin \beta \\0&0&\sin \beta &-\cos \beta \end{pmatrix}}$

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

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