`Show that: sqrt(2+sqrt(2+sqrt(2+2cos8theta)))=2costheta,0 `

Explanation

To show that \( \sqrt{2 + \sqrt{2 + \sqrt{2 + 2 \cos 8\theta}}} = 2 \cos \theta \) for \( 0 < \theta < \frac{\pi}{8} \), we will start with the left-hand side (LHS) and simplify it step by step.

### Step 1: Write down the LHS
We start with the expression:
\[ LHS = \sqrt{2 + \sqrt{2 + \sqrt{2 + 2 \cos 8\theta}}} \]

...