I'm assuming that you meant "3 (csc x)^2 - 4 = 0." Your "csc^2x" is ambiguous.
If 3 (csc x)^2 - 4 = 0, then 3[1/sin x]^2 - 1 = 0 is equivalent. We need to solve this for x.
First, rewrite this as 3[1/sin x]^2 = 4.
Next, divide both sides by 3: [1/sin x]^2 = 4/3
This quadratic equation has two roots, one positive and one negative.
Supposing [1/sin x]^2 = 4/3, then 1/sin x = 2/sqrt(3). Inverting both sides, sin x = sqrt(3)/2. Find x by finding the inverse function:
x=arcsin sqrt(3)/2 so x = 60 degrees, or pi/3 radians.
Now find the other root or roots.
