6 It is given that \(\tan 3 x = k \tan x\), where \(k\) is a constant and \(\tan x \neq 0\).
- By first expanding \(\tan ( 2 x + x )\), show that
$$( 3 k - 1 ) \tan ^ { 2 } x = k - 3$$
- Hence solve the equation \(\tan 3 x = k \tan x\) when \(k = 4\), giving all solutions in the interval \(0 ^ { \circ } < x < 180 ^ { \circ }\).
- Show that the equation \(\tan 3 x = k \tan x\) has no root in the interval \(0 ^ { \circ } < x < 180 ^ { \circ }\) when \(k = 2\).