Summation of trigonometry functions

Geometry Level 4

sin20+sin210+sin220+sin230++sin2180cos20+cos210+cos220+cos230++cos2180\large\dfrac{\sin^2{0^{\circ}}+\sin^2{10^{\circ}}+\sin^2{20^{\circ}}+\sin^2{30^{\circ}}+\ldots+\sin^2{180^{\circ}}}{\cos^2{0^{\circ}}+\cos^2{10^{\circ}}+\cos^2{20^{\circ}}+\cos^2{30^{\circ}}+\ldots+\cos^2{180^{\circ}}}

If the value of the above expression is ab\large\dfrac{a}{b} where aa and bb are coprime positive integers. Find the value of a2+b2a^2+b^2.

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