Shred the cucumber or chop in food processor. Wrap in a towel a squeeze to remove as much water as possible. Mix together the yogurt, shredded cucumber, garlic, white wine vinegar, salt and pepper to taste, and lemon juice. Drizzle lightly with olive oil.
Refrigerate for at least 30 minutes before serving to allow the flavors to meld.
To prepare the chicken, combine the garlic, lemon juice, red wine vinegar, olive oil, yogurt, oregano, and salt and pepper to taste in a medium bowl. Whisk together until mixed well. Add the chicken pieces to the bowl and mix well to coat. Cover and refrigerate for about 1 hour.
Cook the chicken as desired, either in the skillet or with the broiler. Once the chicken is completely cooked through, transfer to a plate and let rest for 5 minutes. Cut into strips. Heat pitas. Top with chicken, tzatziki sauce, diced tomatoes and sliced onions. Serve immediately.
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