Put the tea bags in an 8-cup measuring cup or heat safe bowl. Boil the water, pour it over the tea bags, and allow to steep for at least 10 minutes. Allow to cool and remove tea bags.
In a small saucepan combine the sugar and 1 cup water and bring to a boil. Cook briefly until sugar is dissolved. Remove from heat and add raspberries. Let come to room temperature.
Combine the tea and raspberry sugar syrup, to taste. Put ice into 4 (12-ounce) glasses. To each squeeze in a wedge of lime, pour sugared tea over, and garnish with a sprig of mint.
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