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Algebra on trigonometry

Source: St. Petersburg MO 2001, 11th grade, P1

April 24, 2023
algebratrigonometry

Problem Statement

Do there exist distinct numbers x,y,zx,y,z from [0,π2][0,\dfrac{\pi}{2}], such that six number sin⁡x\sin x, sin⁡y\sin y,sin⁡z\sin z, cos⁡x\cos x, cos⁡y\cos y, cos⁡z\cos z could be partitioned into 3 pairs with equal sums?
[I]Proposed by A. Golovanov
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