Geometry
# Pythagorean Identities

What is the value of

\[ \sin ^2 10 ^ \circ + \sin ^2 20 ^ \circ + \sin ^2 30 ^ \circ + \sin ^2 40 ^ \circ + \sin ^2 50 ^ \circ + \sin ^2 60 ^ \circ + \sin ^2 70 ^ \circ + \sin ^2 80 ^ \circ ? \]

If \( \tan \theta+ \cot \theta = 3 \), what is the value of \( \sin \theta\cos \theta \)?

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