Re: Oh dear
"It takes less than a minute, paper and pencil, with mathematics kids learn when 6 to 7 years..."
I don't know where YOU went to school, but in my country we never studied spherical trig when we were 7. 17 maybe.
The difference is in what kind of "cheater" tables you have, such as Blewitt's book or similar. Having a big book of "cheater" summarisation in a look-up table makes the whole process, as you say, rather simple mathematics - PROVIDED YOU HAVE THE BOOK. (or the newer calculators that have the tables in them!).
But to do it the LONG FORM way, without the aforementioned tables in a book, requires the use of spherical trigonometry, as they did it back in the olden days of wooden ships of the line - Nelson's day. It is tedious, and difficult to get right (lots of chances to mess up the sign of the calculations). I've seen it done a few times, and could not do it myself if I had to. At least not from memory. Even if my life depended upon it.