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A loxodrome maps as a straight line on a Mercator projection map, which does also show true bearing, and Wikipedia tells us that (using a scale of unity) the y coordinate of a given latitude is
ln(sec(φ)+tan(φ))
where φ is the latitude.
As we're using a scale = 1/1, the longitude difference of a circumnavigation is 2*pi. Starting longitude is arbitrary, so that can be mapped at x=0.
On the Mercator map, then, the coordinates are;
(0, -0.282954531434068) and (2*pi, 0.785862966544544)
Calculating the arctan of the slope:
>> atand((0.785862966544544 + 0.282954531434068)/(2*pi))
ans =
9.65403640612811
>> degrees2dms(ans)
ans =
9°39'14.531062"
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