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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