It has been decades since I was friends with trig equations.
So, I threw a bike profile into a CAD program. 39" wheelbase, 16" chainstays, 2" of fork rake.
I came up shy of a .4 degree change, ( using that instead of minutes and seconds for the sake only of keeping what has been discussed congruent) the bottom bracket dropped less than an eighth of an inch.

Changing the fork rake will do much more than the variations of lower headset "stack" heights will effect in a perceptible way.