Non-invasive gamma entrainment has shown promising results in alleviating cognitive symptoms of Alzheimer's disease in mice and humans. In this study, we examine improvements in the synchronization characteristics of the brain's oscillations induced by 40Hz auditory stimulation based on electroencephalography data recorded from a group of dementia patients. We observed that when the quality of entrainment surpasses a certain level, several indicators of brain synchronization significantly improve. Specifically, the entrained oscillatory activity maintains temporal phase stability in the frontal, parietal, and occipital regions, and persistent spatial phase coupling between them. In addition, notable theta-gamma phase-amplitude coupling is observed in these areas. Interestingly, a high theta power at rest predicts the quality of entrainment. We identify differentiating attributes of temporal/spatial synchronization and cross-frequency coupling in the data of two groups with entrained and non-entrained responses which point to enhanced network synchronization caused by entrainment and can explain its potential therapeutic effects.