Step 1: Use the identity
If $\tan A = 1$, $\tan B = \frac{1}{2}$, $\tan C = \frac{1}{3}$, then $\tan(A + B + C) = \dfrac{\Sigma\tan - \Pi\tan}{1 - \Sigma\tan\tan}$.
Step 2: Compute the pieces
Sum of tangents $= 1 + \frac{1}{2} + \frac{1}{3} = \frac{11}{6}$. Product $= \frac{1}{6}$. Sum of pair products $= \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1$.
Step 3: Evaluate
The denominator is $1 - 1 = 0$, so $\tan(A + B + C)$ is undefined, which means the total is $\frac{\pi}{2}$ (numerator $\frac{11}{6} - \frac{1}{6} = \frac{5}{3} \ne 0$).
Step 4: Conclusion
Each angle is acute, so the total lies between 0 and $\frac{3\pi}{2}$, and the only odd multiple of $\frac{\pi}{2}$ in that range is $\frac{\pi}{2}$ itself.
Final Answer:
The total is pi/2. This is option (D).
\[ \boxed{\text{(D) }\frac{\pi}{2}} \]