Let a,b,c be the angles of a triangle. Evaluate\(\begin{vmatrix} \sin^2 A & \cot A & 1 \\ \sin^2 B & \cot B & 1 \\ \sin^2 C & \cot C & 1 \end{vmatrix}.\)
Expanding along the third column, we find that most terms cancel, and we are left with a determinant of 1.
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