How would the phases of the moon change depending on the inclination of its orbit with respect to its primary's equatorial plane? Earth's moon has an orbit that is rather close to the ecliptic, but most natural satellites seem to orbit closer to their primary's equatorial plane.
(Initially I wanted to know what the moon would look like if it had a polar orbit, but it turns out this configuration is unstable due to the Kozai-Lidov mechanism. Is there a "most stable orbit" for natural satellites, some sort of orbital inclination where this effect won't occur? If a natural satellite is on a highly inclined orbit, and if these orbits are unusual, what kind of mechanism can put them there?)
For the purposes of this question, I'm assuming everything else is fairly equal (e.g. Earth-sized primary, Luna-sized moon, and Sol-sized parent star).