Cook the spaghetti until half done; add the broccoli & continue cooking until both pasta & broccoli are al dente. Meanwhile, heat the garlic in the olive oil with the red chili. When the garlic is golden, remove the pan from the heat & remove the bits of chili. Discard the chili & set the oil aside. Drain the pasta & broccoli & toss with the reserved garlic. Season with salt & pepper & serve immediately.