It started in the 2009 draft. The Patriots owned the 73rd pick when the Packers traded up to draft Clay Matthews 26th overall (and kick-started complaints about the Patriots passing on him for the next 3 years), swapping the 41st and 73rd pick to do so. The Patriots ended up using the 41st pick in the draft to select UConn CB Darius Butler. The Patriots had also drafted Patrick Chung, Ron Brace, and Sebastian Vollmer at that point.
Then the Jacksonville Jaguars came calling. With the draft well into the 3rd round, the Patriots had the 73rd, 89th, and 97th picks in the draft. The Jaguars fell in love with a small school CB (William & Mary) named Derek Cox. Despite not being invited to the combine (neither did Vollmer, who went 58th overall in that same draft), the Jaguars felt the guy could be a big player for them in their secondary because the Jaguars were contending for a playoff spot at the time. The two teams struck a deal, with the Jaguars offering a 7th (232) and the following season's 2nd rd pick (ended up becoming the 44th overall pick) to facilitate the deal. Jaguars drafted Cox and the Patriots added a late selection while also beefing up their draft ammo for the following season.
In other words, the Patriots traded the pick that ended up becoming Derek Cox for the picks that ended up becoming Julian Edelman and Rob Gronkowski. Hindsight tells us that Belichick absolutely took Gene Smith to the cleaners in this deal because Cox only played 4 years in Jacksonville while Edelman and Gronkowski turned into top NFL receivers. At the time, the value of the draft picks was pretty close as BB turned a 2009 3rd into a 2010 2nd in a much deeper draft. If you thought a 4th rd pick for Randy Moss in his prime was lopsided, this trade certainly outdoes it in terms of value added to the Patriots. After leaving Jacksonville to sign a 4-year, $20M deal with the Chargers (I felt that Cox would be a good pickup at CB in case the team didn't re-sign Aqib Talib that off-season), but never lived up to that contract due to injuries and inconsistent play. Cox was released after 1 season and did not play for a single NFL team for the 2014 season. The Patriots ended up signing him this off-season to compete for a wide open CB position. I can't say if he'll make the team or not, but he does bring good size and speed to the position at 6'1" 195 and a 4.4 40. At worst, he gets cut in camp and at best could be a surprise contributor.
Edelman and Gronkowski were the top two receivers for the Patriots in 2014 and in Super Bowl XLIX. We can talk ad nauseum how good those two players have become, but that discussion is for a difference post on a different day. With how that 2009 Draft day trade ended up, perhaps the Patriots should fit Cox for a Super Bowl ring simply for being good enough to entice the Jacksonville Jaguars to trade a 2010 2nd (Rob Gronkowski) and a 2009 7th (Julian Edelman) for him.