6 、 Calculate the value of $\cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7} \cos \frac{6 \pi}{7}$ is $\qquad$ .
Answer: $\frac{1}{8}$.
Solution: Let $S=\cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7} \cos \frac{6 \pi}{7}$, then $S=-\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}$, $-S \cdot 8 \sin \frac{\pi}{7}=8 \sin \frac{\pi}{7} \cdot \cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=4 \sin \frac{2 \pi}{7} \cdot \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=2 \sin \frac{4 \pi}{7} \cos \frac{4 \pi}{7}$ $=\sin \frac{8 \pi}{7}=-\sin \frac{\pi}{7}$, therefore, $S=\frac{1}{8}$.