Question 65
Prove that
$$
\sin 10^\circ \cdot \cos 20^\circ \cdot \sin 30^\circ \cdot \cos 40^\circ \cdot \sin 50^\circ \cdot \cos 60^\circ \cdot \sin 70^\circ \cdot \cos 80^\circ = \frac{1}{256}.
$$
$$
\sin 10^\circ \cdot \cos 20^\circ \cdot \sin 30^\circ \cdot \cos 40^\circ \cdot \sin 50^\circ \cdot \cos 60^\circ \cdot \sin 70^\circ \cdot \cos 80^\circ = \frac{1}{256}.
$$