# Trigo Time

Geometry Level 3

$$\large S = sin^{4}(\frac{\pi}{16})+sin^{4}(\frac{3\pi}{16})+sin^{4}(\frac{5\pi}{16})+sin^{4}(\frac{7\pi}{16})$$.

If $$S$$ can be represented in the form $$\dfrac{a}{b}$$ where $$a$$ and $$b$$ are co prime integers

Find $$a \times b$$

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