$\tan 12°.\tan 24°.\tan 48°.\tan 84°=$

$=\frac{\tan 12.\tan \left(60-12\right).\tan \left(60+12\right)\tan 24.\tan \left(60-24\right)\tan \left(60+24\right)}{\tan \left(60+12\right)\tan \left(60-24\right)}$

$=\frac{\tan 3\left(12\right).\tan 3\left(24\right)}{\tan 72.\tan 36}$

$=\frac{\tan 36.\tan 72}{\tan 72.\tan 36}$

$=1$