In spherical coordinates, say $r, \theta, \phi$, is there a matrix representation of rotation of angle $\alpha$ around an arbitrary axis $k$, or around one of the coordinate axis say y. (I say y-axis, as rotation around z-axis is trivial). The Rodriguez formula given in https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula#Matrix_notation gives in cartesian coordinates. What I am looking for is something like the matrix $R$ in $[\theta'~\phi']^t = R(k,\alpha) [\theta ~\phi]^t$, where superscript $t$ stands for transpose, and $\alpha$ is angle of rotation around k.
Is it even possible as rotation in spherical are affine transformations and not orthogonal transformations? If not a matrix transformation, then is there a simple relation between $(\theta', \phi')$ and $(\theta, \phi)$?