Make sure the clams are clean; scrub them with a stiff brush under cold water if you need to. Lay them in a large, wide pot no more than 2 clams deep. Pour over 3/4 cup of white wine. Cover the pot and bring to a boil. Turn the heat down to a simmer and steam open the clams. Pay attention and pluck out each clam as it opens -- this prevents them from being overcooked. Remove the clams from their shells and cut into 2 to 3 pieces. Put them in a bowl with a tablespoon of the olive oil and toss to coat. Set aside for now.
Discard the shells. Strain the liquid in the pan by pouring over a fine-meshed strainer with a paper towel set inside it that has been set over a bowl. Reserve the strained liquid.
Wipe out the pan and add the remaining olive oil. Turn the heat to medium-high and saute the garlic for about 1 minute; don't let it brown. Add the red pepper flakes and the remaining white wine. Boil this for 1 minute, then add the reserved clam juice. Turn off the heat.
Boil the pasta in a large pot of salty water. When it is almost done -- very al dente, as in just barely crunchy in the center -- move the pasta to the pan and turn the heat to high. When it begins to boil, toss the pasta with the sauce constantly so the pasta is evenly coated. Add the reserved clams and the tomatoes while you are doing this. The pasta should be fully cooked in 30 seconds to 1 minute. When it's perfect, turn off the heat and mix in the basil. Serve at once.