Trigonometric Identity?
Express the value of \(S\) as a rational number in lowest terms where
\(sin^2(10^{\circ}) + sin^2(20^{\circ}) + sin^2(30^{\circ}) +\\ sin^2(40^{\circ}) + sin^2(50^{\circ}) + sin^2(60^{\circ}) +\\ sin^2(70^{\circ}) + sin^2(80^{\circ}) + sin^2(90^{\circ}) \\ = S\)
And NO Calculator allowed.
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