# Integration of Legendre Polynomials with different arguments

I'm trying to calculate this:

$$\sum_{l=0}^{\infty} \int_{\Omega} d\theta' d\phi' \cos{\theta'} \sin{\theta'} P_l (\cos{\gamma})$$

where $P_{l}$ are the Legendre polynomials, $\Omega$ is the surface of a sphere of radius $R$, and

$$\cos{\gamma} = \cos{\theta'} \cos{\theta} + \sin{\theta'}\sin{\theta}\,\cos({\phi' -\phi})$$

I am told that only the $l=1$ term survives due to orthogonality of Legendre polynomials (of course $\cos{\theta'} = P_{1}(\cos{\theta'})$), but I'm don't see why, since the Legendre polynomials have different arguments.

How can I show that this is true?
