Preheat oven to 375 F. Cut tomatoes in half and mix with olive oil, garlic, and salt and pepper. Spread on shallow sided baking sheet. Bake for 25-30 minutes.
During last 5 minutes of baking time, prepare angel hair pasta as directed on package. Drain, retaining a small amount of pasta water.
Scrape all bits of tomatoes, garlic and juice into small saucepan being sure to get all you can off the pan. Add dash of red papper flakes and basil. Mix in chicken broth or pasta water if tomatoes did not emit enough juice to mix with pasta. Heat gently for 5 minutes then add pasta.