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sin20∘+sin210∘+sin220∘+sin230∘+…+sin2180∘cos20∘+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}}}cos20∘+cos210∘+cos220∘+cos230∘+…+cos2180∘sin20∘+sin210∘+sin220∘+sin230∘+…+sin2180∘
If the value of the above expression is ab\large\dfrac{a}{b}ba where aaa and bbb are coprime positive integers. Find the value of a2+b2a^2+b^2a2+b2.
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