# Trig Summation

Geometry Level 5

$\frac{\sin{0^{\circ}}+\sin{1^{\circ}}+\sin{2^{\circ}}+\sin{3^{\circ}}+\ldots+\sin{2015^{\circ}}+\sin{2016^{\circ}}}{\cos{0^{\circ}}+\cos{1^{\circ}}+\cos{2^{\circ}}+\cos{3^{\circ}}+\ldots+\cos{2015^{\circ}}+\cos{2016^{\circ}}}$

If the above expression equals $-\sqrt{a+b\sqrt{a}}$ for positive integers $a$ and $b$. Find $a \times b$.

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