Show that the equation

$$3\sin 2x\tan 2x=\cos 2x+2$$

Can be written in the form

$$4{\cos }^{2}2x+2\cos 2x-3=0$$

Find all values for $x$ in the interval $0\le x<180^{\circ }$, for which

$$3\sin 2x\tan 2x=\cos 2x+2$$

Give your answers to two decimal places.