In a small saucepan, bring 2 cups water to a boil. Remove from the heat; add tea bags. Cover and steep for 5 minutes. Discard tea bags.
In a large saucepan, bring sugar and remaining water to a boil. Cook and stir until sugar is dissolved. Remove from the heat; stir in the juices and green tea.
Fill cylinder of ice cream freezer; freeze according to manufacturer's directions. Transfer sorbet to a freezer container; cover and freeze for 4 hours or until firm.
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