Number of Trigonometric solutions

Algebra Level 4

For each integer n>1n>1, let F(n)F(n) be the number of solutions to the equation sinx=sin(nx)\sin{x} = \sin{(nx)} on the interval [0,π][0,\pi]. What is n=22007\displaystyle\sum_{n=2}^{2007}F(n)F(n)?

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