Bring a large pot of salted water to a boil.
In a large, deep-sided skillet over medium heat, heat the olive oil. Add the red pepper flakes and garlic and cook until the garlic is fragrant and golden, 1-2 minutes. Pour in the wine and reduce by half.
Add the diced tomatoes and tomato sauce and stir together, the mussels to the pot and cover. Cook until the mussels have opened wide. Discard any that have not opened.
Add the angel hair to the boiling water and cook till al dente. Use kitchen tongs to divide the pasta between bowls, then top with mussels and sauce. Sprinkle with the fresh basil and serve.