sin x sin y sin (x-y) + sin y sin z sin (y-z) + sin z sin x sin (z-x) + sin (x-y) sin (y-z) sin (z-x)
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take common the sin (x-y) term from 1st & 4th and also take sin z from 2nd & 3rd then simply split the term where you getting the sin z common you will get the answer!!!