I encounter four product of sphrerical harmonic problems and found it has this equation
$Y_{l_1}^{m_1}(\theta,\phi)Y_{l_2}^{m_2}(\theta,\phi) =$
$\displaystyle\sum\limits_{l,m}\sqrt{\frac{(2l_1+1)(2l_2+1)(2l+1)}{4\pi}} \left( {\begin{array}{ccc} l_1 & l_2 & l \\ 0 & 0 & 0 \\ \end{array} } \right) \left( {\begin{array}{ccc} l_1 & l_2 & l \\ m_1 & m_2 & m \\ \end{array} } \right)(-1)^m Y_{l}^{m}(\theta,\phi)$
and then I apply to be this equation
$\int Y_{l_1}^{m_1}(\theta,\phi)Y_{l_2}^{m_2}(\theta,\phi)Y_{l_3}^{m_3}(\theta,\phi)Y_{l_4}^{m_4}(\theta,\phi)\ d\Omega = $
$\displaystyle\sum\limits_{l_{12},m_{12}} \sqrt{\frac{\left(2l_1+1\right)\left(2l_2+1\right)\left(2l_3+1\right)\left(2l_4+1\right)\left(2l_{12}+1\right){}^2}{4\pi }} \left( {\begin{array}{ccc} l_1 & l_2 & l_{12} \\ 0 & 0 & 0 \\ \end{array} } \right) \left( {\begin{array}{ccc} l_1 & l_2 & l_{12} \\ m_1 & m_2 & m_{12} \\ \end{array} } \right)$
$\left( {\begin{array}{ccc} l_3 & l_4 & l_{12} \\ 0 & 0 & 0 \\ \end{array} } \right) \left( {\begin{array}{ccc} l_3 & l_4 & l_{12} \\ m_3 & m_4 & -m_{12} \\ \end{array} } \right)$
Any one can tell me that I am correct ?