Let $A_1, A_2, ..., A_n$ lies on circle $(O)$ such that $A_1A_2=A_2A_3=...=A_nA_1$. Prove that:
$\displaystyle \frac{1}{A_1A_2^2}+\frac{1}{A_1A_3^2}+...+\frac{1}{A_1A_n^2}=\frac{n^2-1}{12R^2}, \forall{n\ge 3}$.