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SMO 2024 Senior Round 1 Question 22

SMO · SMO 2024 Senior Round 1

Question 22

Evaluate the sum $$\frac2{1+\tan\left(\frac\pi{260}\right)}+\frac2{1+\tan\left(\frac{2\pi}{260}\right)}+\frac2{1+\tan\left(\frac{3\pi}{260}\right)}+\cdots+\frac2{1+\tan\left(\frac{129\pi}{260}\right)}.$$