Prove that:
`cotAcot2A-cot2Acot3A-cot3AcotA=1`

Explanation

To prove the equation \( \cot A \cot 2A - \cot 2A \cot 3A - \cot 3A \cot A = 1 \), we will follow a systematic approach using trigonometric identities.

### Step-by-Step Solution:

1. **Rewrite \( \cot 3A \)**:
We can express \( \cot 3A \) using the cotangent addition formula:
\[
\cot 3A = \cot(2A + A) = \frac{\cot 2A \cot A - 1}{\cot 2A + \cot A}
...