The film, called One On One, was shot by French New-Wave director Jean Luc-Godard at Olympic Studios, then largely forgotten. In it you'll see The Stones learning the song, then trying different versions until they hit upon the one that we know today.
They then begin to record it for real, in which you'll see the entire band performing at once. The vocal overdubs are interesting as well, with Jagger singing on one side of gobo and the group background vocals on the other.
You have to watch a 15 second commercial to get to the video, but trust me, it's worth it.
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