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The actor is known to be a fan of the comedy series and made a cameo appearance in its last ever episode.
He said: "The Fast Show might have been one of the most brilliant things in any world - television, theatre, whatever. It was a brilliant show."
Explaining how he managed to secure a guest spot, he said: "When it was mentioned as a possibility, I actively pursued it. I went after [Paul] Whitehouse. I stalked him. I was sitting in a tree outside his bedroom window with a funny mask on and that's how I got the job."
Depp is currently starring in Tim Burton's horror musical Sweeney Todd: The Demon Barber of Fleet Street, which opens in UK cinemas on January 25.
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