A geometry problem by A Former Brilliant Member

Geometry Level 3

Consider a triangle A B C ABC with centroid G G . Evaluate

cot A B C + cot B C A + cot C A B + cot A G B + cot B G C + cot C G A \cot \angle ABC + \cot \angle BCA + \cot \angle CAB \\ + \cot \angle AGB + \cot \angle BGC + \cot \angle CGA


The answer is 0.

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