100 POINTS! NEED HELP QUICKLY! Look at picture below

60, 75

150  165

240   255

330  345

Step-by-step explanation:

csc 4 theta = -2 sqrt(3)/3

Write in terms of sin

1/ sin (4 theta) = -2 sqrt(3)/3

Using cross products

-2 sqrt(3) = 3 sin (4 theta)

Divide each side by 3

-2 sqrt(3)/3 =  sin (4 theta)

Take the inverse sin on each side

sin ^ -1(-2 sqrt(3)/3) = sin ^ -1 (sin (4 theta))

240 +360n = 4 theta

and 300 +360n = 4 theta  where n is an integer

Dividing each side by 4

240/4 +360n/4 = 4/4 theta  and   300/4 +360n/4 = 4/4 theta

60 + 90n = theta      and 75 +90n = theta

We want all the values between 0 and 360

Let n=0

60, 75

n=1

60+90=150  and 75+90 =165

n=2

60+180= 240   75+180=255

n=3

60+270 = 330  75+ 270 =345

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: