How can I prove the following identity?
\begin{equation} \int d\Omega_{\hat k} P_l(\hat n \cdot \hat k) P_{l'}(\hat n'\cdot \hat k)=\frac{4\pi}{2l+1} P_l(\hat n\cdot \hat n')\delta_{ll'}\label{PP} \end{equation}
Both hand-waving one and rigorous one are welcome