Bring chopped fresh pineapple, sugar, and 1 cup water to a boil in a saucepan over medium-high heat. Reduce heat to low; simmer, stirring often, 10 minutes. Cool slightly; process in a blender. Pour through a wire-mesh strainer into a 1-gal. container. Bring 3 cups water to a boil over medium-high heat in a saucepan. Add tea bags; boil 1 minute. Remove from heat; cover and steep 10 minutes. Discard tea bags, and stir tea into pineapple mixture. Stir in 1/4 cup chopped fresh basil and 6 cups cold water. Serve over ice.