 Solution

For $q=2$, at conjunctionThe stable geometry puts conjunctions a quarter orbit from either node, where $M_2$ has maximum vertical separation from the inner body's plane and close approaches are avoided. Therefore ${\lambda }_c-{\Omega }_2=\pi /2$ or $3\pi /2$, and both possibilities giveThis is resonance protection: the resonant phase moves conjunctions away from the two node crossings, where the physical separation would be smallest.