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The temporal variation of the inclination of the axis of rotation produces the alteration in illumination angles over time. Precession impacts which stars rise and set at which time of year, not the angle of inclination. The same gravitational forces that produce the temporal change in inclination of the axis of rotation produce precession, however, the change of angle of the axis alters illumination angles, not precession (a distinct motion).
See: http://www.jqjacobs.net/astro/aegeo.html
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