It is a pity that iteration is needed in this case, because a trig solution can be done directly, without iteration. But this is geometry...
What the old RAF navigators don't tell you is that the winds aloft forecast is usually so much in error that the precision possible with the slide rule (or any other exact calculation method) is wasted.
A simple rule of thumb is as good.
At higher speeds, accuracy is less important because the wind effect on the plane is smaller.
Also, it is damn hard to fly a heading to within a few degrees, by hand, for long periods.
And the final nail in the coffin of precise wind calcs is that if you plan reasonably short inter-waypoint distances, say less than 20nm, it is hard to get lost anyway - provided you have chosen clean and unambiguously identifiable ground features. When some early pioneer flew from the USA to the UK, he had to only fly a heading within 10 degrees to hit Ireland, and after that it was a piece of cake. Even the crudest sextant will give you latitude good enough for that. And if you have chosen ambiguous features then you
will get lost no matter how accurately you fly, because the visual waypoint identification will naturally take precedence over the calculated heading
GPS has made all this largely redundant.
Mrs DFC will be around in a minute to set us amateurs straight, I am sure