In a bowl, toss the berries with 1/2 cup of the sugar. Cover with plastic wrap and let stand at room temperature for 4 hours or refrigerate overnight; stir occasionally until the sugar is dissolved and the strawberries are very juicy.
In a small saucepan, combine the remaining 1 cup of sugar with the water and citrus zests. Bring to a boil over moderate heat and cook just until the sugar dissolves, stirring occasionally; let the citrus syrup cool.
Strain the citrus syrup into a medium glass or ceramic bowl. Strain the strawberry juice into the syrup and add the orange and lemon juices.
In a food processor, combine one-third of the strawberries with 1/2 cup of the syrup and puree until smooth. Stir the strawberry puree into the syrup and freeze for 30 minutes. Using a fork, stir the ice crystals that form around the edges into the liquidy center and return to the freezer. Continue to stir and freeze until the mixture resembles soft snow, about 40 minutes. Stir in the remaining strawberries, freeze until just firm but not solid and serve.
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