The value of magnetic course is calculated according to (2).
Corrected course can be determined by summing measured value of magnetic course [psi] with compensation value for course [phi] calculated from GPS data [[psi].
With navigation constructed around magnetic courses, lacking reliable magnetic indication causes interesting navigation problems.
The FAA uses grid and magnetic courses for approaches north of approximately the Arctic Circle, but all other published FAA courses are still referenced to magnetic north.
The GPS calculates the magnetic course
by conjuring the great circle route based upon the lat/long value of two VORs, and then adds the local magnetic variation at the aircraft's present position.
Likewise, a minor amendment could change charted magnetic courses
due to magnetic variation since the ground track remains the same.