You can use the trig identity and factor
you have (tan2x/1-tan2x) + tanx = 0
You find a common denominator of 1-tan2x
this gives you: tan2x + (tanx)(1-tan2x) = 0
(this equation is all over '1-tan2x', but you can get rid of it by moving it to the other side of the '=' sign, and multiplying this by the 0).
You then expand the brackets to get: tan2x + tanx - tan3x = 0
You then simplify this to get: tan3x + tanx = 0
Hope this helps.