Peel the cucumber, then cut in half lengthwise. Seed it, and coarsely chop it.
In a bowl, combine the garlic, salt, lemon juice, pomegranate molasses, 1 tablespoon of sumac and 4 tablespoons of olive oil.
In a separate bowl, combine the sumac with 2 tablespoons of olive oil.
Separate the pita bread in two thinner flat breads to obtain 6 thin flat breads total. Brush them with the sumac and olive oil, then cut them in 1-inch squares. Toast them in an oven preheated at 400 F.
The pita bread can alternatively be fried. To do so, preheat 1 cup of oil in a skillet and fry the pita bread pieces until golden, for about 1 minute. Drain on a plate lined with paper towel.
In a large bowl, combine all the vegetables and greens. Pour the dressing, and sprinkle with a little sumac.
Add the toasted or fried pita bread right before serving, and toss well.