Find the value of 2 cos² 45° + 3 tan² 60° - 4 sin² 30°.

The special angles: $\sin 0^\circ = 0$, $\sin 30^\circ = \dfrac{1}{2}$, $\sin 45^\circ = \dfrac{1}{\sqrt{2}}$, $\sin 60^\circ = \dfrac{\sqrt{3}}{2}$, $\sin 90^\circ = 1$; the cosines are the same values in the opposite order. $\tan 30^\circ = \dfrac{1}{\sqrt{3}}$, $\tan 45^\circ = 1$, $\tan 60^\circ = \sqrt{3}$, and $\tan 90^\circ$ is not defined.