IMO 1986 LL USS78

If T and T1 are two triangles with angles x, y, z and x1, y1, z1,

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IMO 1986 LL USS78

Origin: USS

Problem

If T and T1 are two triangles with angles x, y, z and x1, y1, z1, respectively, prove the inequality cos x1 sin x + cos y1 sin y + cos z1 sin z \leqcot x + cot y + cot z.