For example during the calculation of the scattering cross section for the process $e^+ e^- \rightarrow \mu^+ \mu^-$ it can be established that for spin-$\frac{1}{2}$ particles, the angular distribution of the scattered particles has the form

$$ \frac{dN}{d\Omega} \propto 1 + \cos^2\theta $$

where $\theta$ is the angle between the $\mu^{\pm}$ and the beam direction.

Does there exist an elegant general relationship or function that describes the dependence of the angular distribution of the scattered particles on their spin?

Or can one do no better than looking at particles of different spins (0, 1, 3/2, 2, ...) case by case and calculate the corresponding scattering cross sections to find the angular distribution in each case?