Prove that `1+cot theta <= cot (theta/2) `for `0 < theta < pi`. Find `theta` when equality signs holds.

Explanation

To prove that \(1 + \cot \theta \leq \cot \left(\frac{\theta}{2}\right)\) for \(0 < \theta < \pi\), we will follow these steps:

### Step 1: Rewrite the Inequality
We start with the inequality:
\[ 1 + \cot \theta \leq \cot \left(\frac{\theta}{2}\right) \]
Rearranging gives us:
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