Solution:

$\therefore 70^{o} - 20^{o} = 50^{o}$

$\tan \left(70^{\circ}-20^{\circ}\right)=\tan 50^{\circ}$

$\frac{\tan 70^{\circ}-\tan 20^{\circ}}{1+\tan 70^{\circ} \tan 20^{\circ}}=\tan 50^{\circ}$

$\tan 70^{\circ}-\tan 20^{\circ}=\tan 50^{\circ}\left(1+\tan 70^{\circ} \tan 20^{\circ}\right)$

$\tan 70^{\circ}-\tan 20^{\circ}=\tan 50^{\circ}+\tan 50^{\circ} \tan 70^{\circ} \tan 20^{\circ}$

$\tan 70^{\circ}-\tan 50^{\circ}-\tan 20^{\circ}=\tan 70^{\circ} \tan 50^{\circ} \tan 20^{\circ}$