Determining the rotation angle and normal for a rotation through Euler angles

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[1] pr. 3.9 poses the problem to determine the total rotation angle for a set of Euler rotations given by

\begin{equation}\label{eqn:eulerAngleRotationAngleAndNormal:20} \mathcal{D}^{1/2}(\alpha, \beta, \gamma) = \begin{bmatrix} e^{-i(\alpha+\gamma)/2} \cos \frac{\beta}{2} & -e^{-i(\alpha-\gamma)/2} \sin \frac{\beta}{2} \\ e^{i(\alpha-\gamm…