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clemire

Is there an error here? How did sin theta d-theta d-phi turn into d cos theta d-phi?

Tianye

Remember that $d cos\theta = -sin\theta d \theta$.

Therefore, $\int_0^{\pi}sin\theta d\theta = -\int_1^{-1}d cos\theta = \int_{-1}^1 d cos\theta$

The integration in terms of $\phi$ remains unchanged