The value of $\sqrt{2+\sqrt{2+\sqrt{2+2\cos 8\theta}}}$ where $\theta < \theta<\large\frac{\pi}{8}$ is equal to

Question

$(a)\;2\cos\theta\qquad(b)\;\cos\theta\qquad(c)\;2\sin\theta\qquad(d)\;-2\cos\theta$