Given:

\(\tan(\theta - \phi) = 3\)

\(\tan \theta + \tan \phi = 1\)

Using the tangent subtraction formula:

\(\tan(\theta - \phi) = \frac{\tan \theta - \tan \phi}{1 + \tan \theta \tan \phi} = 3\)

Substitute \(\tan \theta + \tan \phi = 1\) into the equation:

\(\frac{\tan \theta - (1 - \tan \theta)}{1 + \tan \theta (1 - \tan \theta)} = 3\)

Simplify:

\(\frac{2\tan \theta - 1}{1 + \tan \theta - \tan^2 \theta} = 3\)

Cross-multiply and simplify:

\(2\tan \theta - 1 = 3(1 + \tan \theta - \tan^2 \theta)\)

\(2\tan \theta - 1 = 3 + 3\tan \theta - 3\tan^2 \theta\)

Rearrange to form a quadratic equation:

\(3\tan^2 \theta - \tan \theta - 4 = 0\)

Solving this quadratic equation gives:

\(\tan \theta = 1.5 \quad \text{or} \quad \tan \theta = -\frac{4}{3}\)

For \(\tan \theta = 1.5\), \(\theta \approx 56.3^\circ\) or \(236.3^\circ\) (only \(56.3^\circ\) is valid).

For \(\tan \theta = -\frac{4}{3}\), \(\theta \approx 126.9^\circ\) or \(306.9^\circ\) (only \(126.9^\circ\) is valid).

Using \(\tan \theta + \tan \phi = 1\), find \(\phi\):

For \(\theta = 56.3^\circ\), \(\phi \approx 161.6^\circ\).

For \(\theta = 126.9^\circ\), \(\phi \approx 63.4^\circ\).

Thus, the possible pairs are \((\theta, \phi) = (135^\circ, 63.4^\circ)\) and \((53.1^\circ, 161.6^\circ)\).