Preheat the oven to 425 degrees F.
Stack the pita and, using a sharp serrated knife, cut into 6 wedges. Place the wedges in a large metal mixing bowl. Drizzle in the olive oil. Using metal tongs, toss the pita to coat evenly. Sprinkle in the sesame seeds, thyme, oregano, sumac, salt and pepper; toss to distribute the seasonings evenly.
Transfer the pita to a baking sheet and spread uniformly to ensure even browning. Place into the oven and bake until golden brown, 5 to 7 minutes. Remove and cool slightly.
Sumac can be found in the spice section on the baking aisle of your local grocer or at a spice market.