# Summation of trigonometry functions

Geometry Level 4

$\large\dfrac{\sin^2{0^{\circ}}+\sin^2{10^{\circ}}+\sin^2{20^{\circ}}+\sin^2{30^{\circ}}+\ldots+\sin^2{180^{\circ}}}{\cos^2{0^{\circ}}+\cos^2{10^{\circ}}+\cos^2{20^{\circ}}+\cos^2{30^{\circ}}+\ldots+\cos^2{180^{\circ}}}$

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

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