Prove that tan⁡−113+tan⁡−115+tan⁡−117+tan⁡−118=π4.\text{Prove that } \tan^{-1} \frac{1}{3} + \tan^{-1} \frac{1}{5} + \tan^{-1} \frac{1}{7} + \tan^{-1} \frac{1}{8} = \frac{\pi}{4}.

Mathematics

Problem

Prove that tan⁡−113+tan⁡−115+tan⁡−117+tan⁡−118=π4.\text{Prove that } \tan^{-1} \frac{1}{3} + \tan^{-1} \frac{1}{5} + \tan^{-1} \frac{1}{7} + \tan^{-1} \frac{1}{8} = \frac{\pi}{4}.

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