Solve : `5cos2theta+2cos^2(theta/2)+1=0,-pi lt theta lt pi`

Explanation

To solve the equation \(5\cos(2\theta) + 2\cos^2\left(\frac{\theta}{2}\right) + 1 = 0\) for \(-\pi < \theta < \pi\), we can follow these steps:

### Step 1: Use the double angle identity
We know that:
\[ \cos(2\theta) = 2\cos^2(\theta) - 1 \]
Substituting this into the equation gives:
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