(i) Show that the equation \(\tan(45^\circ + x) = 2 \tan(45^\circ - x)\) can be written in the form \(\tan^2 x - 6 \tan x + 1 = 0\).

(ii) Hence solve the equation \(\tan(45^\circ + x) = 2 \tan(45^\circ - x)\), for \(0^\circ < x < 90^\circ\).