Prove that, \( \cos \theta \cos 2 \theta \cos 2^{2} \theta \ldots \...

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Prove that, \( \cos \theta \cos 2 \theta \cos 2^{2} \theta \ldots \cos 2^{n-1} \theta=\frac{\sin 2^{n} \theta}{2^{n} \sin \theta} \), for all \( n \in \mathbf{N} \).
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