Well, I must be doing something right because looking that up I find the Arctic Circle lies at 66.5622 deg. North, i.e. 23.4378 deg. South of the North Pole!
Now, the angle of the path of the sun to the plane of the horizon is dependent on the latitude. My latitude is 36.87 S approx.
You can see from the diagram that the ">23.4 deg" distance will get greater as you go South as the path of the sun flattens with respect to the horizon, until at the pole it is parallel.
This is where it has to go to Mathematics for a value for my latitude, and I see if I can make this highly capable computer actually do a few computations for me!
A check on the web gives me first, an approximation: -
North and South of the Equator the deviation is larger by a factor 1/cos(latitude) The approximation breaks down at large latitudes - it does pretty much OK up to about 50 degrees North or South. (We should be OK with this at 36.87 deg. Sth.)
Then the full formula: -
The full calculation using spherical geometry (derivation) gives the angle from due west on the solstice as arcsin(sin(23.4)/cos(L)). ( I don't think we need to go there do we?)
Thanks to Windows' bundled Calculator, which I have just discovered has a Scientific mode (Apparently it has been there since Windows 3.0, 1990, 24 years and I have not noticed!!), Cos(36.87) = 0.7999989281485085293299423897698 and the reciprocal is 1.2500016747701993040919584188775, lets call it 1.25 near enough :-)
So the ANSWER is:
(23.4 + 1.25) x 2 = 49.3 degrees
I've been thinking about the ridiculous 31 decimal places in the calculator results.
To put it in perspective, 10^31 in metres is the lower bound of the (possibly infinite) radius of the universe.