Show that the equation
$$\tan \left( 45 ^ { \circ } + x \right) = 4 \tan \left( 45 ^ { \circ } - x \right)$$
can be written in the form
$$3 \tan ^ { 2 } x - 10 \tan x + 3 = 0$$
Hence solve the equation
$$\tan \left( 45 ^ { \circ } + x \right) = 4 \tan \left( 45 ^ { \circ } - x \right)$$
for \(0 ^ { \circ } < x < 90 ^ { \circ }\).