Show that `sqrt(2+sqrt(2 +2 cos 4 theta))= 2 cos theta`

Explanation

To prove that \(\sqrt{2 + \sqrt{2 + 2 \cos 4\theta}} = 2 \cos \theta\), we will start with the left-hand side (LHS) and simplify it step by step.

### Step 1: Write down the LHS
\[ \text{LHS} = \sqrt{2 + \sqrt{2 + 2 \cos 4\theta}} \]

### Step 2: Simplify the inner square root
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