# So Many Solutions!?

Level pending

Find the last 3 digits of the number of solutions to $\sin x+\cos^2 x+\cos^3 x+\sin^4 x+\sin^5 x+...+\cos^{99}x+\sin^{100} x = \frac{121 \sqrt3}{2}$ for $$x \in [-100 \pi, 100 \pi]$$

Note that the for the power $$n$$, we add $$\sin^n x$$ if $$x \equiv 1, 4 \pmod 4$$ and we add $$\cos^n x$$ if $$x \equiv 2, 3 \pmod 4$$

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