(i) Show that the equation \(\tan(x - 60^\circ) + \cot x = \sqrt{3}\) can be written in the form \(2 \tan^2 x + (\sqrt{3}) \tan x - 1 = 0\).

(ii) Hence solve the equation \(\tan(x - 60^\circ) + \cot x = \sqrt{3}\), for \(0^\circ < x < 180^\circ\).