I have to calculate Roll, Pitch and Yaw angles from a $3\times3$ rotation matrix (below).
\begin{bmatrix}0&\frac{1}{2}&-{\frac{\sqrt{3}}{2}}\\0&-{\frac{\sqrt{3}}{2}}&-\frac{1}{2}\\-1&0&0\end{bmatrix}
I know how to calculate second angle:
$\theta = \arcsin (N_z) = \arcsin(-(-1)) = 90^{\circ}$
but the other angles seem to be impossible to calculate:
$\phi = \arctan \dfrac{N_y}{N_x} = \arctan \dfrac{0}{0}$
$\psi = \arctan \dfrac{O_z}{A_z} = \arctan \dfrac{0}{0}$
since theta is $90$ degrees I know:
$\psi - \phi = \arctan\dfrac{O_z}{A_z} = \arctan\dfrac{\frac{1}{2}}{\frac{-\sqrt{3}}{2}} = 150^{\circ}$
How to calculate these angles?