We use the tangent addition formula:
\[
\tan(\theta + \phi) = \frac\tan \theta + \tan \phi1 - \tan \theta \tan \phi
\]
Substitute \(\tan \theta = \frac12\) and \(\tan \phi = \frac13\):
\[
\tan(\theta + \phi) = \frac\frac12 + \frac131 - \frac12 \frac13
\]
Simplify numerator: \(\frac12 + \frac13 = \frac3 + 26 = \frac56\)
Simplify denominator: \(1 - \frac16 = \frac56\)
Thus: \(\tan(\theta + \phi) = \frac\frac56\frac56 = 1\)
Since \(\tan(\theta + \phi) = 1\), \(\theta + \phi = \frac\pi4\) (principal value).
Hence, the correct answer is (D) \(\frac\pi4\).