Trig Summation

Geometry Level 5

sin0+sin1+sin2+sin3++sin2015+sin2016cos0+cos1+cos2+cos3++cos2015+cos2016\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 a+ba-\sqrt{a+b\sqrt{a}} for positive integers aa and bb. Find a×ba \times b.

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