Trig Summation

Geometry Level 4

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

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

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