Find the area of the shaded region

Can somebody please help me with this?

I know that θ = -pi/2 to pi/2, but I don't know how the radius is changing. I need to make a double integral in polar coordinates as far as I can tell.

Can somebody please help me and explain?

http://i42.tinypic.com/otm5o3.png

Thank you.

A = 1/2 ∫(0~2π)(4+2sins)^2 dx =>18π
but shaded part is half,
so, 9π is my answer.
is it right ?