Product formula for cosines

Identity. We use repeatedly $2\cos x\sin x=\sin 2x$, i.e. $\cos x=\frac{\sin 2x}{2\sin x}$:
$$\cos\theta=\frac{\sin2\theta}{2\sin\theta},\quad \cos2\theta=\frac{\sin4\theta}{2\sin2\theta},\quad \cos4\theta=\frac{\sin8\theta}{2\sin4\theta}.$$

Product.
$$\cos\theta\cos2\theta\cos4\theta=\frac{\sin8\theta}{8\sin\theta}.$$

Conclusion. $\cos\theta\cos2\theta\cos4\theta=\frac{\sin8\theta}{8\sin\theta}$.