@PM2Ring If you are interested, I have further generalised my calculation in the answer to work with all latitudes and not just at the equator and the maximum latitude. I also managed to get ChatJax to work in Google Chrome in Windows (still not working in Microsoft Edge).

@KDP I'm kind of busy with other things. I had a quick look at your updated answer. It seems ok, but you should explain the relation between latitude / declination phi and the parametric latitude beta.