2007 AMC 12A 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 \qquad \mathrm{(B)}\ 2015028 \qquad \mathrm{(C)}\ 2015033 \qquad \mathrm{(D)}\ 2016532 \qquad \mathrm{(E)}\ 2017033

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.