Good ol' trigonometry (KVPY)

Geometry Level 4

csc2(a+b)sin2(ba)+sin2(2ab)=cos2(ab) \large \csc^2 (a+b) - \sin^2 (b-a) + \sin^2 (2a-b) = \cos^2 (a-b)

The equation above holds true for 0<a,b<π20<a,b< \dfrac\pi2. Find the value of sin(ab) -\sin(a-b) .

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