Stir sugar and water in heavy medium saucepan over medium heat untill sugar dissolves. Increase heat; boil until syrup turns deep amber, occasionally brushing down sides of pan with wet pastry brush and swirling pan, 8 minutes. Remove from heat. Mix in vinegar (mixture will bubble vigorously). Add juice and shallots: Boil until reduced to 3/4 cup, stirring occasionally, 15 minutes. Add broth: boil until reduced to 1 cup, 30 minutes. Set aside.
Using small knife, cut off peel and white pith from 4 oranges. Working over bowl, cut between membranes to release segments. (Sauce and oranges can be prepared 6 hours ahead. Cover separately; chill.)
Using small knife, score duck skin (do not pierce meat) in crosshatch pattern. Sprinkle duck with salt and pepper. Heat heavy large skillet over medium-high heat. Place duck breasts skin down in skillet. Cook until brown and crisp, about 8 minutes. Turn duck and cook 2 minutes more and transfer to baking dish. Bake in a 450 degree oven for 5 to 7 minutes, about 10 minutes longer for medium-rare. Transfer to cutting board. Let stand 10 minutes. Meanwhile, bring sauce to simmer. Add butter and 1 tablespoon grated orange peel; whisk just until butter melts. Drain orange segments and mix into sauce. Set aside. Slice duck breasts crosswise on diagonal. Arrange on 6 plates. Spoon orange segments with sauce alongside. Sprinkle with remaining peel.
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