St. Petersburg Mathematical Olympiad Problem 1

Geometry Level 3

Do there exist distinct numbers x,y,z[0,π/2]x,y,z\in[0,\pi /2] such that the six numbers sinx,siny,sinz,cosx,cosy,cosz\sin x, \sin y, \sin z, \cos x, \cos y, \cos z can be divided into three pairs with equal sum?

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