Problem

Source: China TST 2002 Quiz

Tags: inequalities, trigonometry, geometry unsolved, geometry



In acute triangle $ ABC$, show that: $ \sin^3{A}\cos^2{(B - C)} + \sin^3{B}\cos^2{(C - A)} + \sin^3{C}\cos^2{(A - B)} \leq 3\sin{A} \sin{B} \sin{C}$ and find out when the equality holds.