solve the given trigonometric equation exactly over the inte

solve the given trigonometric equation exactly over the interval,

0<(or equal to) thetha <(or equal to) 2pi. csc^2(theta) - csc(theta) - 2 = 0

a) 7/6pi, 11/6pi, 1//2pi

b) 1/6pi, 11/6pi, 1/2pi

c) 7/6pi, 5/6pi, 3/2pi

d) 1/6pi, 5/6pi, 3/2pi

This is a quadratic equation, so factoring

This will give two values of csc

csc = -1 and csc = 2

As we know, sin = 1 / csc

Which means

sin = -1 and sin = 1/2

referring the unit circle

At is 3pi/2 sin is -1

Similarly, At = pi/6 & 5pi/6, sin is 1/2

So the answer = pi/6, 5pi/6 and 3pi/2. Option (d)