Prove that `cos^2x+cos^2(x+pi/3)+cos^2(x-pi/3)=3/2`.

Explanation

To prove that \( \cos^2 x + \cos^2 \left( x + \frac{\pi}{3} \right) + \cos^2 \left( x - \frac{\pi}{3} \right) = \frac{3}{2} \), we will start by simplifying the left-hand side step by step.

### Step 1: Write down the expression
We start with the expression:
\[ LHS = \cos^2 x + \cos^2 \left( x + \frac{\pi}{3} \right) + \cos^2 \left( x - \frac{\pi}{3} \right) \]

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