(a(i))[3]
Demonstrate that the equation $\tan(x - 60^\circ) + \cot x = \sqrt{3}$ can be rearranged into the form $2\tan^2 x + (\sqrt{3})\tan x - 1 = 0$.
(a(ii))[3]
Hence, solve the equation $\tan(x - 60^\circ) + \cot x = \sqrt{3}$ for $0^\circ < x < 180^\circ$.