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Put all the ingredients into a large freezer bag, including the drumsticks. Coat them with the marinade and refrigerate for 30 minutes.
Preheat oven to 350°F (180°C). Place the drumsticks on a baking sheet lined with parchment paper and bake for about 45 minutes. Check doneness on one of the drumsticks and return to the oven as needed.
Serve hot with a legume salad, with raisin couscous or with jasmine rice, green onions and red peppers.