Just trying to find what theta is between for the boundary (x^2)+(y^2)-y=0 in polar coordinates

the whole problem is:

Evaluate the surface area of the portion of the sphere (x^2)+(y^2)+(z^2)=1 that is inside the cylinder (x^2)+(y^2)-y=0. Hint; the double integral can be evaluated in polar coordinates

I put the sphere in polar coordinates and got the double integral of ((1-r^2)^-1/2) r d(r) d(theta) which is correct according to my answer sheet.

Then to find the limits of r I put the cylinder in polar coordinates and got r(r-sin(theta)) = 0. So 0<=r<=sin(theta)

But how would I find the limits of theta for the circle in the xy-plane (x^2)+(y-(1/2))^2 = 1/4 ? (I believe that circle equation is equivalent after completing the square)