The enhanced transport of trapped energetic ions (TEIs) in the presence of resonant interactions between trapped fast ions and a rotating magnetic island is investigated within a drift-kinetic framework. Gyro-orbit banana center model equations of resonances between the island rotation, the bounce motion of trapped fast ions, and their precession frequency (poloidal precession and precession in the helical direction) are constructed. There are two solutions for resonances in phase space for different mode numbers, with only one solution having low-energy resonant lines (< 100 keV); the other h...