（12）观察下列等式：
$\left(\sin \frac{\pi}{3}\right)^{-2}+\left(\sin \frac{2 \pi}{3}\right)^{-2}=\frac{4}{3} \times 1 \times 2$ ；
$\left(\sin \frac{\pi}{5}\right)^{-2}+\left(\sin \frac{2 \pi}{5}\right)^{-2}+\left(\sin \frac{3 \pi}{5}\right)^{-2}+\left(\sin \frac{4 \pi}{5}\right)^{-2}=\frac{4}{3} \times 2 \times 3 ;$
$\left(\sin \frac{\pi}{7}\right)^{-2}+\left(\sin \frac{2 \pi}{7}\right)^{-2}+\left(\sin \frac{3 \pi}{7}\right)^{-2}+\cdots+\left(\sin \frac{6 \pi}{7}\right)^{-2}=\frac{4}{3} \times 3 \times 4 ;$
$\left(\sin \frac{\pi}{9}\right)^{-2}+\left(\sin \frac{2 \pi}{9}\right)^{-2}+\left(\sin \frac{3 \pi}{9}\right)^{-2}+\cdots+\left(\sin \frac{8 \pi}{9}\right)^{-2}=\frac{4}{3} \times 4 \times 5 ;$
照此规律，$\left(\sin \frac{\pi}{2 n+1}\right)^{-2}+\left(\sin \frac{2 \pi}{2 n+1}\right)^{-2}+\left(\sin \frac{3 \pi}{2 n+1}\right)^{-2}+\cdots+\left(\sin \frac{2 n \pi}{2 n+1}\right)^{-2}=$ $\_\_\_\_$ ．
$\frac{4}{3} \times n \times(n+1)$