Start with the equation:

\(6 \cos \theta \tan \theta - 3 \cos \theta + 4 \tan \theta - 2 = 0\)

Factorise by grouping:

\(3 \cos \theta (2 \tan \theta - 1) + 2 (2 \tan \theta - 1) = 0\)

Factor out \((2 \tan \theta - 1)\):

\((2 \tan \theta - 1)(3 \cos \theta + 2) = 0\)

Set each factor to zero:

\(2 \tan \theta - 1 = 0\) or \(3 \cos \theta + 2 = 0\)

Solve for \(\theta\):

\(\tan \theta = \frac{1}{2}\)

\(\theta = \tan^{-1}\left(\frac{1}{2}\right) \approx 26.6^\circ\)

\(\cos \theta = -\frac{2}{3}\)

\(\theta = \cos^{-1}\left(-\frac{2}{3}\right) \approx 131.8^\circ\)

Thus, the solutions are \(\theta = 26.6^\circ\) and \(\theta = 131.8^\circ\).