Double Symmetrical

Geometry Level 4

Find the sum

tan(a)tan(2a)+tan(2a)tan(3a)++tan(8a)tan(9a),\tan (a) \tan (2a) + \tan(2a) \tan(3a) +\cdots+ \tan(8a) \tan(9a),

where a=π5.a=\frac{\pi}{5}.

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