How to prove this identity

Question

tan3x - tan2x- tanx = tan3xtan2xtanx

Answer 1

tan3x - tan2x- tanx=tan(2x+x)-tan2x-tanx=(tan2x+tanx)/(1-tan2xtanx)-(tan2x+tanx)

=(tan2x+tanx)(1/(1-tan2xtanx)-1)=(tan2x+tanx)(1-(1-tan2xtanx))/(1-tan2xtanx)

=(tan2x+tanx)(tan2xtanx/(1-tan2xtanx)=[(tan2x+tanx)/(1-tan2xtanx)]tan2xtanx=tan3xtan2xtanx