Prove that $\sin A - \sin B + \sin C = 4\sin A/2 \cos B/2 \sin C/2$

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Prove that $\sin A - \sin B + \sin C = 4\sin A/2 \cos B/2 \sin C/2$ occurs in an $ABC$ triangle. I don't know how to solve the RHS... Can anyone help me please?

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Hint: Use the Half Angle identities to simplify the right side into terms of A, B, and C. After that, it should be much easier.