If `cot(alpha+beta)=0\ ,\ ` then write the value of `"sin"(alpha+2beta)` .

Explanation

To solve the problem, we need to find the value of \( \sin(\alpha + 2\beta) \) given that \( \cot(\alpha + \beta) = 0 \).

### Step-by-Step Solution:

1. **Understanding the Condition**:
We know that \( \cot(\theta) = 0 \) when \( \theta = \frac{\pi}{2} + n\pi \) for any integer \( n \). Therefore, we can set:
\[
\alpha + \beta = \frac{\pi}{2}
...