Comment (by Zach Etienne):

I adjusted the sampled points so that 0 and n{x,y} correspond to points that lie within (0,pi), and (0,2 pi), excluding the endpoints (midpoints, naturally). dtheta and dphi were adjusted accordingly.

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Ticket URL: https://bitbucket.org/einsteintoolkit/tickets/issues/2282/gallery-examples-use-low-order-integration