Season the shrimp. In a bowl, toss the shrimp with 1 tablespoon olive oil, a good pinch of sea salt, and freshly ground pepper. Set aside.
Warm the garlic and chili. Pour 2 tablespoons olive oil into a large, deep skillet over low heat. Add half the garlic and the chili peppers and cook, stirring, until fragrant, about 1 minute. Don't let the garlic brown.
Sear the shrimp and add the ouzo. Raise the heat to medium-high, add the shrimp, and cook, stirring occasionally, until they turn pink on the outside, about 2 minutes. They'll finish cooking in the sauce. Take the pan off the heat, pour in the ouzo, then return it to the heat for about 1 minute, until the alcohol cooks off. Lift the shrimp out with a slotted spoon onto a plate, leaving the pan juices in the skillet.
Cook the tomatoes. Add the remaining olive oil and garlic to the skillet, then the cherry tomatoes. Sprinkle the sugar and a pinch of salt over the tomatoes. Cook over medium-low heat, stirring occasionally, until the tomatoes burst, release their juices, and turn saucy, 25 to 30 minutes. Press a few with the back of a spoon to help them along.
Cook the spaghetti. While the tomatoes cook, bring a large pot of well-salted water to a boil. Cook the spaghetti until al dente, about 10 minutes (or according to the package). Scoop out 1 cup of pasta water before you drain anything.
Finish the shrimp. Return the shrimp and any juices on the plate to the tomato sauce and simmer on low just until the shrimp are opaque throughout (145°F/63°C), 1 to 2 minutes.
Toss with the pasta and feta. Set the pasta pot next to the skillet and use tongs to transfer the spaghetti straight into the sauce. A little pasta water coming along is a good thing. Take the pan off the heat, add the feta, and toss well. Add a splash of pasta water to loosen the sauce if needed. Season with salt and pepper to taste.
Serve. Serve in pasta bowls with chopped fresh basil and a drizzle of olive oil.