Determine exact solution. x E (0, 2pi)

Question

2csc^2x-8=0

Answer 1

2csc^2x-8=0
csc^2 x = 4/2 = 4
then
sin^2 x = 1/4
sinx = ±1/2 ---> so x can be in any of the 4 quads
we know sinπ/6 = 1/2

so
x = π/6
x = π - π/6 = 5π/6
x = π + π/6 = 7π/6
x = 2π - π/6 = 11π/6