1989 OIM Problems/Problem 2

Problem

Let $x$, $y$, $z$ three real numbers such that $0<x<y<z<\frac{\pi}{2}$. Prove the following inequality: \[\frac{\pi}{2}+2sin(x)cos(y)+2sin(y)cos(z) > sin(2x)+sin(2y)+sin(2z)\]

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe4.htm