In triangle `A B C ,tan(A-B)+tan(B-C)+"tan"(C-A=0.` Prove that the triangle isisoceles.

Explanation

To prove that triangle ABC is isosceles given that \( \tan(A-B) + \tan(B-C) + \tan(C-A) = 0 \), we will follow these steps:

### Step 1: Use the tangent subtraction formula
We start by using the tangent subtraction formula:
\[ \tan(A-B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} \]
Let \( \tan A = p \), \( \tan B = q \), and \( \tan C = r \). Then we can rewrite the equation as:
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