Step 1:
We can use the formula for the difference of two sines, which is given by:
$$
\sin a - \sin b = 2 \cos \left(\frac{a+b}{2}\right) \sin \left(\frac{a-b}{2}\right)
$$
So, we can rewrite the given expression as:
$$
\sin \frac{\theta}{2}-\sin \frac{3 \theta}{2}
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