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How to prove this identity

Sin 3x + sin2x - sinx = 4sinxcos(x/2)cos(3x/2)

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sin 3x  + sin 2x - sin x
 
= sin3x + 2cos(3x/2)sin(x/2)
 
= 2sin(3x/2)cos(3x/2). + 2cos(3x/2)sin(x/2)
 
= 2cos(3x/2)[sin(3x/2) + sin(x/2)]
 
= 2 cos(3x/2)[2sin( x) cos (x/2)]
 
= 4sinx cos (x/2) cos (3x/2)