I thought I had implemented #Meeus's Earth #nutation algorithm incorrectly, because it gives -3.808 for Δψ (nutation in longitude) instead of -3.788 for the example. So I checked my implementation carefully for errors. Found an error in the Moon's argument of longitude. Not enough to make a difference. Found an error in the coefficient table, but it was a coefficient used only in Δε (nutation in obliquity). So I figured it must be precision related, so I converted everything to use Python's decimal type, along with the sine and cosine implementations from https://docs.python.org/3/library/decimal.html . Same result. So either there's an error in the book, I'm somehow missing some error in the implementation, or the example actually uses the low-precision version of the algorithm that he gives. If it's this last, that would be annoying, because the high-precision version has a lot more room for mistakes.

Time to find someone else's implementation and compare the results.

I had thought the formula #Meeus gives for #SiderealTime must be inaccurate due to the uneven length of the day, but then I realized that it only gives the value for Greenwich at 0 UT, which is always corrected for the Earth's rotation and thus only dependent on the Earth's position in its orbit. Which changes slowly enough that ΔT (the difference between #UniversalTime, which is non-uniform, and a uniform clock, generally #TerrestrialTime) can't have a significant effect.

If the difference really matters to you, you can use the #EarthRotationAngle, which is the current standard for #Astronomy but that seems to be a lot more involved to compute, and it requires downloading data from the #IERS.

#MathematicalAstronomy