By Petra Epperlein and Michael Tucker for the New York Times. Months after the United States invaded Iraq in 2003, I began filming the U.S. Army’s 2nd Battalion, 3rd Field Artillery Regiment in Baghdad. The unit was housed in a bombed-out palace on the banks of the Tigris that they named Gunner Palace. Rather than just making a movie about the men, I suggested that we make a film together — an offer that the...