In triangle `A B C ,` if `cotA ,cotB ,cotC` are in `AdotPdot,` then `a^2,b^2,c^2` are in ____________ progression.

Explanation

To solve the problem, we need to show that if \( \cot A, \cot B, \cot C \) are in arithmetic progression (AP), then \( a^2, b^2, c^2 \) are in arithmetic progression as well.

### Step-by-Step Solution:

1. **Understanding the Condition**:
Given that \( \cot A, \cot B, \cot C \) are in AP, we can express this condition mathematically:
\[
\cot B = \frac{\cot A + \cot C}{2}
...