First express all functions in terms of sines and cosines.
2 sin2t/cos2t = 3/cos t
2 sin2t = 3 cos t
2(1 - cos2t) = 3 cos t
2 cos2t = 3 cos t - 2 =0
This quadratic has one extraneous root and cos t = 1/2
In the interval from 0 to 2 pi, cos 60 and cos 300 both equal 1/2