AMC 12 2007a Problem 24

For each integer $n>1$, let $F(n)$ be the number of solutions to the equation $\sin{x}=\sin{(nx)}$ on the interval $[0,\pi]$. What is $\sum_{n=2}^{2007} F(n)$?

$\mathrm{(A)}\ 2014524 \mathrm{(B)}\ 2015028 \mathrm{(C)}\ 2015033 \mathrm{(D)}\ 2016532 \mathrm{(E)}\ 2017033$