Question 1040321
I would go the other way
csc=2 sqrt(3)/3 is 2/sqrt(3)
Therefore the sin is sqrt (3)/2
That occurs at pi/3 and 2pi/3  on the interval 0 to 2 pi (which covers the above.
With the calculator, try entering 3/(2sqrt(3))
You should get 0.8660.
if you enter 3/2 sqrt(3), the calculator will make that 1.5 *sqrt(3), and you can't take the arc sin of it, because it is greater than 1.