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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),tan(a)tan(2a)+tan(2a)tan(3a)+⋯+tan(8a)tan(9a),
where a=π5.a=\frac{\pi}{5}.a=5π.
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