The F.B.I. has significantly increased its use of stings in terrorism cases, employing agents and informants to pose as jihadists, bomb makers, gun dealers or online friends" in hundreds of investigations. Undercover operations, once seen as a last resort, are now used in about two of every three prosecutions involving people suspected of supporting the Islamic State, a sharp rise in the span of just two years. F.B.I. operatives coax suspects into saying and doing things that they might not otherwise do - the essence of entrapment. "They're manufacturing terrorism cases," said Michael German, a former undercover agent with the F.B.I.. Despite dozens of challenges to undercover terrorism cases brought since the Sept. 11, 2001, attacks, a judge has yet to throw one out on the grounds of entrapment. Not that some judges have not considered it. "I believe beyond a shadow of a doubt that there would have been no crime here, except the government instigated it, planned it and brought it to fruition," Judge Colleen McMahon of the United States District Court ... said in 2011 in a case involving four Muslim men in Newburgh, N.Y. The F.B.I. planted an undercover informant inside a mosque in Newburgh as part of what became an elaborate, nearly yearlong plot. The F.B.I. even built a fake Stinger missile and had it delivered to the men. Judge McMahon said she was troubled by the F.B.I.'s conduct, but she upheld the charges.