The A.M of all the solutions of $4{\cos }^{3}x-4{\cos }^{2}x-\cos \left(\pi +x\right)+1=0in\left(0,315\right)is$

$4{\cos }^{3}x-4{\cos }^{2}x-\cos (x+\pi )-1=0$

$4{\cos }^{3}x-4{\cos }^{2}x+\cos x-1=0$

$4{\cos }^{2}x\left(\cos x-1\right)+1\left(\cos x-1\right)=0$

$$\begin{gathered} \cos x=1 \\ hassolutionsasx=2\pi ,4\pi ,8\pi ,....100\pi in(0,315) \end{gathered}$$ 

$\therefore A.M=\frac{sumofnumbers}{no.ofnumbers}=\frac{2\pi +4\pi +\mathrm{......}+100\pi }{50}=51\pi$