Prove that: `\ sqrt(2+sqrt(2+2cos4theta))=2costheta`

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 manipulate it to reach the right-hand side (RHS).

### Step-by-step Solution:

1. **Start with the LHS:**
\[ \text{LHS} = \sqrt{2 + \sqrt{2 + 2 \cos 4\theta}} \]
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