(a) Show that the equation \(\frac{\tan x + \cos x}{\tan x - \cos x} = k\), where \(k\) is a constant, can be expressed as \((k + 1) \sin^2 x + (k - 1) \sin x - (k + 1) = 0\).

(b) Hence solve the equation \(\frac{\tan x + \cos x}{\tan x - \cos x} = 4\) for \(0^\circ \leq x \leq 360^\circ\).