Question 8
Let $\omega = \cos\frac{2\pi}{7} + i \cdot \sin\frac{2\pi}{7},$ where $i = \sqrt{-1}.$ Find the value of the product $$
\prod_{k=0}^{6} \left(\omega^{3k} + \omega^k + 1\right).
$$
\prod_{k=0}^{6} \left(\omega^{3k} + \omega^k + 1\right).
$$