Bring a large pot of lightly salted water to a rolling boil. Cook the spaghetti at a boil, stirring occasionally, until the tender yet firm to the bite, about 12 minutes; drain and set aside.
Heat olive oil in a large saucepan over medium heat; cook and stir the spinach and mushrooms in the hot oil until they give off their liquid, about 10 minutes.
Add the red wine vinegar and balsamic vinegar; bring to a boil. Stir the tomatoes, basil, parsley, and black olives into the boiling mixture; continue cooking and stirring, until the flavors blend, about 10 more minutes.
Mix the cooked spaghetti into the tomato mixture and reduce heat to medium-low. Simmer the pasta and sauce until the flavors have blended, 8 to 10 minutes; stir the feta cheese into the pasta.
