Verified answer

replace cos^2 = 1 - sin^2 and solve

cos(t)^2 = 1 - sin(t)^2

2 * cos(2t)^2 = 3 * sin(2t)

2 * (1 - sin(2t)^2) = 3 * sin(2t)

2 - 2 * sin(2t)^2 = 3 * sin(2t)

2 * sin(2t)^2 + 3 * sin(2t) - 2 = 0

sin(2t) = (-3 +/- sqrt(9 + 16)) / 4

sin(2t) = (-3 +/- 5) / 4

sin(2t) = -8/4 , 2/4

sin(2t) = -2 , 1/2

sin(2t) cannot equal -2, so that's extraneous

sin(2t) = 1/2

sin(2t) = sin(30) , sin(150) , sin(390) , sin(510)

2t = 30 , 150 , 390 , 510

t = 15 , 75 , 195 , 255

sec(t)^2 = a million + tan(t)^2 sec(t)^2 + tan(t) = a million a million + tan(t)^2 + tan(t) = a million tan(t)^2 + tan(t) = 0 tan(t) * (tan(t) + a million) = 0 tan(t) = 0 t = 0 , a hundred and eighty tan(t) + a million = 0 tan(t) = -a million t = one hundred thirty five , 315 t = 0 , one hundred thirty five , a hundred and eighty , 315