Give a stream of consciousness and then the final answer. The Beatles at Shea Stadium is a fifty-minute-long documentary of the Beatles' 15 August 1965, concert at Shea Stadium in New York City, the highlight of the group's 1965 tour. The documentary was produced by Ed Sullivan (under his Sullivan Productions banner), NEMS Enterprises (which owns the 1965 copyright), and the Beatles company Subafilms. The project, placed under the direction of manager of production operations M. Clay Adams, was filmed by a large crew led by cinematographer Andrew Laszlo. Fourteen cameras were used to capture the euphoria and mass hysteria that was Beatlemania in America in 1965. The documentary first aired on BBC1 on 1 March 1966. In West Germany, it aired on 2 August that year. It aired in the United States on ABC on 10 January 1967.

Answer this question: when did the beatles play at shea stadium?
The important part for answering this question is: The Beatles at Shea Stadium is a fifty-minute-long documentary of the Beatles' 15 August 1965, concert at Shea Stadium in New York City, the highlight of the group's 1965 tour.
So, the final answer is 15 August 1965.