I'm trying to figure out the the area inside the outer loop and above the x axis for the polar curve r = 1 - 2sin(theta).

i think the integral goes from pi to pi/6. I want to say that the integral for the area is 1/2 (1-2sin(theta))^2 d(theta) multiplied by 2 but I'm really not sure. Can someone clarify this for me?