First of all, if , then .
Since this is in Quadrant 2, you know .
You have
where
.
The only solution that lies in is
.
I have spent hours trying to figure out this problem. I know how to get sin2θ, given sinθ, but not the other way around:
Find sinθ, given that sin2θ = -2/3, (3pi/2) < 2θ < 2pi.
The answer is sq(18 - 6sq(5)) / 6.
Thanks for any help.