Bring 3 cups water and first 3 ingredients to a boil in a medium saucepan, stirring until sugar dissolves. Remove pan from heat, and add tea bags. Steep 10 minutes; remove tea bags, and let cool.
Combine tea mixture, rum, and next 5 ingredients in a large container. Chill 1 hour or until ready to serve. Stir in Mandarin orange, lemon, and starfruit slices just before serving.
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