Homework Help: Intersection pts of polar equations

1. The problem statement, all variables and given/known data
I have to find the area of the region that lies inside the curves:

r = sin(θ)
r = sin(2θ)


3. The attempt at a solution

I'm assuming the first step would be to find the points of intersection so I know WHERE to integrate from/to, so I set the equations equal to each other:

sin(θ) = sin(2θ)


arcsin both sides:
θ = 2θ

And I'm stuck. Analysis of the graph shows that the most crucial intersection point occurs at or very close to 75º, but I would like to be able to show that.

 

Thanks a lot! In that case...

sin(θ) = 2sin(θ)cos(θ)
1 = 2cos(θ)
cos(θ) = 1/2
θ = π/3

That should help me get the rest of the problem, thanks again! =]