So confused! Please help with Trig! Solve the equation on the interval

Solve the equation on the interval 0 less than or equal to theta less than 2pi.

cot^2 theta= 3/2 csc theta

cot^2 theta = -5/2 csc theta -2

1)
t = pi/6 || t = (5 pi)/6

2)

t = (7 pi)/6 || t = (11 pi)/6

cot^2x = 3/2cscx
csc^2x - 1 = 3/2cscx
csc^2x - 3cscx/2 - 1 = 0
2csc^2x - 3cscx - 2 = 0
(2cscx + 1)(cscx - 2) = 0
2cscx + 1 = 0 or cscx - 2 = 0
cscx = -1/2 or cscx = 2
sinx = -2 or sinx = 1/2
Discard sinx = -2 because it has no real solutions, leaving just
sinx = 1/2
x = pi/6 or x = 5pi/6

Solve the other similarly.