4. $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7}=$ $\qquad$
4. $\frac{1}{8}$.

Let $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7}=-\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=m$, then $m \cdot 8 \sin \frac{\pi}{7}=-8 \sin \frac{\pi}{7} \cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=-4 \sin \frac{2 \pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=-2 \sin \frac{4 \pi}{7} \cos \frac{4 \pi}{7}=-\sin \frac{8 \pi}{7}=\sin \frac{\pi}{7}$. Therefore, $m=\frac{1}{8}$.