Prove that \[ \cos \theta \cos \frac{\theta}{2}-\cos 3 \theta \cos ...

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Prove that
\[
\cos \theta \cos \frac{\theta}{2}-\cos 3 \theta \cos \frac{9 \theta}{2}=\sin \frac{7 \theta}{2} \sin 4 \theta \text {. }
\]
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