Prove that :$\tan 70 - \tan 20 = 2\tan 40 + 4\tan 10$ Prove that :$\tan 70 - \tan 20 = 2\tan 40 + 4\tan 10$
My Attempt, 
$$70-20=40+10$$
$$\tan (70-20)=\tan (40+10)$$
$$\dfrac {\tan 70 - \tan 20}{1+\tan 70. \tan 20 }=\dfrac 
{\tan 40 + \tan 10 }{1-\tan 40. \tan 10 }$$ 
How should I move on?  Please help 
Thanks 

Left side -
$\tan 70 - \tan 20$
$=  \tan(90 - 20) - \tan 20$
$ = \cot 20 - \tan 20$
$= \frac{\cos^2 20 - \sin^2 20}{\cos 20 \sin 20}$
$ = \frac{\cos 40}{\frac12 \sin 40}$
$ = 2 \cot 40$
Similarly solve for right side.
