# Number of Trigonometric solutions

Algebra Level 4

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 $$\displaystyle\sum_{n=2}^{2007}$$$$F(n)$$?

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