Reserve a handful of the basil leaves plus 8 small sprigs to use as garnish. In a medium saucepan, bring 1 1/2 cups water, the sugar and the remaining basil to a boil. Lower the heat and simmer, stirring, until the sugar is dissolved, about 5 minutes; let cool slightly, then refrigerate until cold. Strain into a clean container, pressing down on the basil to extract any liquids; discard the basil.
In a pitcher, combine the basil syrup, gin, lemon juice and triple sec. Stir in the basil leaves and lemon and orange slices. Serve in tall glasses over ice, topped with a sprig of basil.