(a) Show that the equation \(\cot^2 \theta + 2 \cos 2\theta = 4\) can be written in the form \(4 \sin^4 \theta + 3 \sin^2 \theta - 1 = 0\).

(b) Hence solve the equation \(\cot^2 \theta + 2 \cos 2\theta = 4\), for \(0^\circ < \theta < 360^\circ\).