Prove that: `"cot"pi/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)`

Explanation

To prove that \( \cot \frac{\pi}{24} = \sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{6} \), we will follow a systematic approach using trigonometric identities and calculations.

### Step 1: Express \( \cot \frac{\pi}{24} \) in terms of \( \cot \frac{\pi}{12} \)

We know that:
\[ \cot \frac{\pi}{24} = \cot \left( \frac{\pi}{12} \cdot \frac{1}{2} \right) \]
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