For anyone who was confused like me about why the d(theta) integral bound only goes from pi to 0 rather than 2pi to 0 around the circle, it is because spherical coordinates define theta to just be [0,pi] since the [pi, 2pi) range is already covered by the phi values, i.e. rotating a semicircle all the way around its diameter carves out a full sphere
https://mathinsight.org/spherical_coordinates
For anyone who was confused like me about why the d(theta) integral bound only goes from pi to 0 rather than 2pi to 0 around the circle, it is because spherical coordinates define theta to just be [0,pi] since the [pi, 2pi) range is already covered by the phi values, i.e. rotating a semicircle all the way around its diameter carves out a full sphere https://mathinsight.org/spherical_coordinates
Thank you Woojin!