How did The Beatles overcome tragedy?

By mutually supporting each other, by support from their families and friends, and by channelling their grief into creative effort by writing new songs and lyrics, or just by playing music privately for therapeutic reasons. In the late '60s, they also gained comfort from Eastern religions such as Hinduism and Buddhism, and the self-help teachings they give such as meditation and mindfulness. Sometimes they also took drugs, or went on retreat to claim time out and reflect upon what had happened, and come to terms with it in their own way.