Find all solutions to the equation $\tan x + \tan 2x = 0$ where $0^\circ  \le x < 360^\circ$.

$\tan x + \tan 2x = 0$

$\tan x + \frac{{2\tan x}}{{1 - {{\tan }^2}x}} = 0$     M1

$\tan x - {\tan ^3}x + 2\tan x = 0$     A1

$\tan x(3 - {\tan ^2}x) = 0$     (M1)

$\tan x = 0 \Rightarrow x = 0,{\text{ }}x = 180^\circ$     A1

Note:     If $x = 360^\circ$ seen anywhere award A0

$\tan x = \sqrt 3  \Rightarrow x = 60^\circ ,{\text{ }}240^\circ$     A1

$\tan x =  - \sqrt 3  \Rightarrow x = 120^\circ ,{\text{ }}300^\circ$     A1

[6 marks]