The value of $\cos \left(\frac{2\pi }{7}\right)+\cos \left(\frac{4\pi }{7}\right)+\cos \left(\frac{6\pi }{7}\right)$ is equal to :

$\begin{array}{l}\cos \frac{2\pi }{7}+\cos \frac{4\pi }{7}+\cos \frac{6\pi }{7}\\ \boxed{\cos \alpha +\cos \left(\alpha +\beta \right)+\cos (\alpha +2\beta )+....\cos \left(\alpha +\left(n-1\right)\beta \right)=\frac{\sin {\displaystyle \frac{n\beta }{2}}}{\sin \frac{\beta }{2}}\cos \left(\alpha +\frac{\left(n-1\right)\beta }{2}\right)}\\ =\frac{\sin \left(3\times \frac{\pi }{7}\right)}{\sin \frac{\pi }{7}}\times \cos \left(\frac{\frac{2\pi }{7}+\frac{6\pi }{7}}{2}\right)\\ \\ =\frac{2\sin \left(\frac{3\pi }{7}\right)}{2\sin \frac{\pi }{7}}\times \cos \left(\frac{4\pi }{7}\right)\\ \\ =\frac{\sin \left(\frac{7\pi }{7}\right)+\sin \left(\frac{-\pi }{7}\right)}{2\sin \frac{\pi }{7}}\\ \\ =\frac{-\sin \frac{\pi }{7}}{2\sin \frac{\pi }{7}}\\ =-\frac{1}{2}\\ \mathrm{Option} \mathrm{B} \mathrm{is} \mathrm{correct}\end{array}$