In a pot of salted boiling water cook the shrimp to an internal temperature of 120 degrees using a thermometer, about 2 to 5 minutes depending on size. Drain well, then slice, and set aside to cool.
Preheat the oven to 350 degrees. Toss the pita with oil, chili powder, salt, and pepper. Place on a parchment paper lined baking sheet and drizzle with lime juice. Bake in the oven until golden brown and crispy. Then set aside. Pita will continue to crisp up as it cools.
Mix the shrimp with the remaining ingredients in a bowl. Season with salt and pepper. Refrigerate for 20 to 45 minutes.
Serve the shrimp with pita. Garnish with cilantro.