IMO 1988 LL IRE49

Let −1 < x < 1. Show that

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IMO 1988 LL IRE49

Origin: IRE

Problem

Let −1 < x < 1. Show that  k=0 1 −x2 1 −2x cos(2\pik/7) + x2 = 7(1 + x7) 1 −x7 . Deduce that csc2 \pi 7 + csc2 2\pi 7 + csc2 3\pi 7 = 8.