First, we will use the sum and difference formulas for sine:
$$\sin(a - b) = \sin a \cos b - \cos a \sin b$$
$$\sin(a + b) = \sin a \cos b + \cos a \sin b$$
Now, we will substitute these formulas into the given identity:
$$\sin(a - b) \sin(a + b) = (\sin a \cos
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