hi everyone. I am stuck on which identity to apply next. I know what the next step should look like but I cant get there. could you show which idntity to apply and how? thanks

$\displaystyle tan2x-cotx=0$

$\displaystyle \frac {2tanx}{1-tan^2x}-cotx=0$

$\displaystyle (\frac {1-tan^2x}{1})\frac {2tanx}{1-tan^2x}=cotx(\frac {1-tan^2x}{1})$

$\displaystyle 2tanx=cotx-cotxtan^2x$

this is where I get stuck. how do you get to the next step? it should look like this.

$\displaystyle 2tanx=cotx-tanx$