Answer
The function $\tan 2t $ is discontinuous at $$ t=\frac{(2n+1)\pi}{4}$$
and the discontinuity is infinite.
Work Step by Step
Since $\tan 2t=\frac{\sin 2t }{\cos 2t}$, then the function is discontinuous when
$$\cos 2t =0.$$
That is, $2t=\frac{(2n+1)\pi}{2}$, n is integer. This means that the function $\tan 2t $ is discontinuous at $$ t=\frac{(2n+1)\pi}{4}$$
and the discontinuity is infinite.
