Shred the cabbages and mix them together in a large bowl
Chop the onions and set aside.
Whisk together olive oil, vinegar, oregano, onion powder, garlic powder, salt, pepper and basil in small bowl.
Add onions to dressing mixture and let sit for 1 minute.
Add dressing to cabbage and stir thoroughly to coat.
Add feta and stir.
Refrigerate until chilled and serve!
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