\[\int_{0}^{\pi}P_{l_{1}}\left(\cos\theta\right)P_{l_{2}}\left(\cos\theta\right)%
P_{l_{3}}\left(\cos\theta\right)\sin\theta\,\mathrm{d}\theta=2\begin{pmatrix}l%
_{1}&l_{2}&l_{3}\\
0&0&0\end{pmatrix}^{2},\]