Complex sentence: On 27 January 1933, while dancing at the Cocoanut Grove nightclub, he was arrested for breach of his visa, as part of a general crackdown against illegal immigrants in the film industry.
Split into simpler sentences: On 27 January 1933 he was arrested while dancing at the Cocoanut Grove nightclub for breach of his visa. This was part of a general crackdown against illegal immigrants in the film industry.