Complex sentence: In addition to small vaudeville shows, the three brothers landed jobs in the Broadway musical "The Great Waltz", during which time Lew Christensen became a student at Balanchine's new School of American Ballet.
Split into simpler sentences: In addition to their small vaudeville shows, they landed a job in the Broadway musical "The Great Waltz". During this time Lew Christensen became a student at the new School of American Ballet.