Angels & Demons isn’t even out yet, but already Hollywood is salivating at the idea of a third Robert Langdon film from Dan Brown…

Tom Hanks has been making a name for himself as Robert Langdon, the protagonist of Ron Howard’s duo of puzzle film novel adaptations, The Da Vinci Code (May 2006) and Angels & Demons (May 2009). Everyone seems to think that these movies have a built in audience thanks to the best-selling novels, so everyone is ready to get behind a trilogy-capper. Only one problem, no one has seen the third book in the Robert Langdon series as of yet:

Author Dan Brown has announced that his next installment in the “Da Vinci Code” series will be “The Lost Symbol,” which Doubleday will publish in the U.S. and Canada on Sept. 15. The first print run will be a whopping 5 million copies. Much more than that will be needed if the sales of “Angels and Demons” and “Da Vinci Code” are anything to go by.

“Angels and Demons” has sold 39 million copies to date, and that number is certain to go up following the book’s recent reemergence on the New York Times bestseller list in anticipation of the film’s release. Those sales lag behind “The Da Vinci Code,” whose 81 million copies sold puts it behind the Bible but not much else.

Sources said Brown has completed his manuscript. Sony has the rights to the Robert Langdon character, which gives the studio the right to negotiate a deal for the new title. The studio will be bullish. “The Da Vinci Code” grossed $758 million worldwide in 2006, and Columbia has high hopes for the sequel produced by Imagine topper Brian Grazer and John Calley. Brown is exec producer.

Call me crazy, but I think this is the way we’re going to get original stories into the Hollywood system these days. Like when Thomas Harris was so pressured to write a sequel to Silence of the Lambs after the film hit it big that he wrote Hannibal to be virtually unfilmable, forcing the flick to expand in weird and unexpected directions, most notably: brain-eating.

If Dan Brown makes The Lost Symbol as factually inaccurate as the previous two outings, I’m pretty sure I won’t be learning anything new about the Masons. However, bringing The Da Vinci Code so boldly and deliberately into National Treasure territory might be interesting too.