> 
> Prove the identity 
>  $$8\cos^4 \theta -4\cos^3 \theta-8\cos^2 \theta+3\cos \theta +1=\cos4\theta-\cos3\theta$$
> 
> 
> If $7\theta $ is a multiple of $2\pi,$ Show that $\cos4\theta=\cos3\theta$ and deduce, 
>  $$\cos\frac{2\pi}{7}+\cos\frac{4\pi}{7}+\cos\frac{6\pi}{7}=-\frac{1}{2}$$
> 
> 
> 

**My Work**

I was able to prove identity using half angle formula and $\cos3\theta $ expansion.
Since 

$$7\theta=2n\pi$$ $$4\theta=2n\pi-3\theta$$

$$\therefore \cos4\theta=\cos3\theta$$

> 
> I cannot prove the final part. 
> 
> 
> 

Please help me. Thanks in advance.