Find all the angles between 0 degrees and 360 degrees which will satisf y the equation:
5tan^2 y +5 tan y = 2 sec^2 y
recalling that sec^2 = 1+tan^2, rearrange things to have
3tan^2 y + 5 tan y - 2 = 0
(3tan y - 1)(tan y + 2) = 0
tan y = 1/3 or -2
tan is positive in QI and QIII, so tany = 1/3 means that
y = 18.43° or 198.43°
tany = -2 means
y = 116.57° or 296.57°