Squared signed sum

Geometry

What is the value of

sin⁡210∘+sin⁡220∘+sin⁡230∘+sin⁡240∘+sin⁡250∘+sin⁡260∘+sin⁡270∘+sin⁡280∘? \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 ?

Arron Kau by Arron Kau
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