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Let $0, $0<\lambda<1, \mu=1-\lambda$. Does anyone see a good proof of the inequality:

$\sin(\lambda a)\sin(\lambda b)+\sin(\lambda a)\sin(\mu b)\cos(b)+\sin(\lambda b)\sin(\mu a)\cos(a)+\sin(\mu a)\sin(\mu b)>\sin(a)\sin(b).$

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    The LHS equals the RHS for $a=b=\pi/4,\lambda=\mu=1/2$.2015-12-19

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