# 2015-19 Sum of tangent functions

Evaluate $\sum_{k=0}^{n} 2^k \tan \frac{\pi}{4\cdot 2^{n-k}}.$

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# 2012-17 Two Tangent Functions in a Series

Let $$m$$ and $$n$$ be odd integers. Determine $\sum_{k=1}^\infty \frac{1}{k^2}\tan\frac{k\pi}{m}\tan \frac{k\pi}{n}.$

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