How can an arbitrary rotation matrix
$R = \left(\begin{matrix} R_{11} & R_{12} & R_{13} \\ R_{21} & R_{22} & R_{23} \\ R_{31} & R_{32} & R_{33}\end{matrix}\right)$
be decomposed into the equivalent fixed-axis zxz Euler angles ($\theta,\phi,\psi$)?
I understand the decomposition into the equivalent body-axis Euler angles, but I don't follow the decomposition for the fixed-axis situation.