I need to evaluate integrals of this form
$\int\limits_{\phi = 0}^{2\pi }\ \int\limits_{\theta = 0}^{\pi} \left | f_1(\theta, \phi)e^{ix} + f_2(\theta, \phi)e^{ix'} \right |^2\sin{\theta} \ d\theta d\phi$
Where,
$f_1$ and $f_2$ are harmonic functions of $\theta$ and $\phi$. Mostly, $\cos^2{\frac{\theta}{2}}$ or $\sin^2{\frac{\theta}{2}}$ and in general, $f_1 \neq f_2$. $x$ and $x'$ are some real constants.
Any help regarding how I can evaluate these integrals is highly appreciated.