Question

If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \), where \( A + B + C = \pi \), then what is the value of \( \tan A \tan B + \tan B \tan C + \tan C \tan A \)?

• A. 1
• B. 0
• C. 2
• D. Cannot be determined

Hint:

\textbf{Tip:} When \( A + B + C = \pi \), the identity \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \) implies that the pairwise product sum is 1.