 What about the poles though? At the poles, the person isn't travelling along the circular route anymore, so I'd expect that the centripetal acceleration should be zero. If the person were up at the north pole, 90 degrees north of the equator, then theta would be equal to 90 minus 90, or zero, and sine of zero is zero, so the centripetal acceleration would be zero. So our answer at 28 degrees, which is in between these two, seems reasonable.