Prove that: `cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1`

Explanation

To prove that \( \cot x \cot 2x - \cot 2x \cot 3x - \cot 3x \cot x = 1 \), we will use the cotangent addition formula.

### Step-by-Step Solution:

1. **Rewrite \( \cot 3x \)**:
We can express \( \cot 3x \) as \( \cot(x + 2x) \). Using the cotangent addition formula:
\[
\cot(a + b) = \frac{\cot a \cot b - 1}{\cot a + \cot b}
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