\( 4\cot^2\theta - 2\cot\theta = 3(1 + \cot^2\theta) \)
\( 4\cot^2\theta - 2\cot\theta - 3 - 3\cot^2\theta = 0 \)
\( \cot^2\theta - 2\cot\theta - 3 = 0 \)

\( (\cot\theta - 3)(\cot\theta + 1) = 0 \)
\( \cot\theta = 3 \) or \( \cot\theta = -1 \)

\( \tan\theta = \dfrac{1}{3} \) or \( \tan\theta = -1 \)

For \( \tan\theta = \dfrac{1}{3} \): \( \theta = 18.43^\circ \) and \( 180^\circ + 18.43^\circ = 198.43^\circ \)
For \( \tan\theta = -1 \): \( \theta = 135^\circ \) and \( 315^\circ \)

\(\boxed{\theta = 18.4^\circ,\; 135^\circ,\; 198.4^\circ,\; 315^\circ}\)