Preheat the oven to 350 degrees F. For the pita chips, line a baking sheet with foil and place pita triangles on the prepared sheet. Place the olive oil in a small bowl then brush it over the cut pita. Sprinkle with the listed herbs and spices to your liking. Bake pita chips for 8-12 minutes, or until golden brown and crunchy. Watch them carefully after 8 minutes as they can burn quickly.
For the tzatziki, slice the cucumber in half lengthwise and scoop out the seeds using a spoon. Grate the cucumber and place in a fine-sieve strainer. Squeeze as much liquid out of the cucumber then sprinkle with salt. Let stand over the sink for 30 minutes then squeeze again to get remaining liquid out. Meanwhile, mix garlic, dill, yogurt and lemon juice together. Stir in the shredded cucumber. Place in an airtight container and refrigerate until ready for use.
For the gyro meat, combine the beef, garlic, onion, salt and pepper in a bowl. Divide beef into 8 equal portions and shape into patties. Add olive oil to a skillet over medium-high heat. Place patties in the skillet and cook until browned, 2 to 3 minutes, then flip and cook another 2 to 3 minutes or until cooked through.
To assemble: divide the rice equally between 4 bowls. Top each bowl 1/4 of the tzatziki, 2 pita chips, 2 beef patties and tomatoes.