# Infinite Trigonometric Sums Part 1

Geometry Level 3

The infinite sum below when $$x=\frac{\pi}{6}$$ can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a^{2}+b^{2}$$?

$$\sin x - 2 \sin^{2} x + 3 \sin^{3} x - 4 \sin^{4} x + 5 \sin^{5} x - 6 \sin^{6} x +\ldots$$

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