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Meanwhile, in a large, heavy skillet heat the olive oil over medium heat. Add the garlic, red pepper flakes, salt and pepper and saute for 3 minutes. Add the clams, mussels, and wine. Cook for 5 minutes, making sure all the shells have opened. Discard any shells that remain closed. Sprinkle with the parsley.
In a large bowl, toss together the pasta, broccoli, and shellfish. Add the reserved pasta water, 1/4 cup at a time, to moisten. Toss to combine. Transfer to a serving platter and serve immediately.