Let A,B,C, be three angles such that `A=pi/4` and `tanB tanC=pdot` Find all possible values of `p` such that `A , B ,C` are the angles of a triangle.

Explanation

To solve the problem, we need to find all possible values of \( p \) such that the angles \( A, B, C \) can form a triangle given that \( A = \frac{\pi}{4} \) and \( \tan B \tan C = p \).

### Step-by-Step Solution:

1. **Understanding the Triangle Angle Sum**:
Since \( A, B, C \) are the angles of a triangle, we know that:
\[
A + B + C = \pi
...