Practice your tangent sum and difference formula!
If \( \tan A = \frac 1 2 \) and \( \tan B = \frac 1 3 \), find the values of \( \tan(2A+B) \) and \( \tan (2A- B) \) respectively.
Details and Assumptions:
- The choices depicts the two values: \( \tan(2A +B) \) and \( \tan(2A-B) \) in that order.
Bonus: If we know that only one of the choices given is definitely correct, determine which one of it is correct without manually computing any of the two values in question.