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 \( 0 < \theta < \pi \) and to find the value of \( \theta \) when equality holds, we can follow these steps:

### Step 1: Rewrite the inequality
We start with the inequality:
\[ 1 + \cot \theta \leq \cot \left( \frac{\theta}{2} \right) \]
This can be rearranged to:
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