  Single spin state evolution induced by the
Landau-Zener-St\"uckelberg-Majorana (LZSM) interference in a Zeeman-spit four
level system in a periodically driven double quantum dot is studied
theoretically by the Floquet stroboscopic method. An interplay between
spin-conserving and spin-flip tunneling processes with the Electric Dipole Spin
Resonance (EDSR) that is induced in an individual dot and enhanced by the LZSM
multiple level crossings with the neighboring quantum dot is investigated as a
function of the microwave (MW) frequency, driving amplitude, interdot detuning,
and magnetic field. A number of special points in the parameter space are
identified, out of which where all the three features are merged. Under this
triple-crossing resonance condition the interdot tunneling is combined with a
fast spin evolution in each dot at the EDSR frequency. Harmonics of the EDSR
are revealed in the spin-dependent tunneling maps versus variable magnetic
field and MW frequency. The results are applicable for both electron and hole
systems with strong spin-orbit interaction and may be useful for developing new
time-efficient schemes of the spin control and readout in qubit devices.
