For the pita chips. Preheat the oven to 400 degrees F.
Slice the pita in half through the pocket, then into chip-size triangles. Lay the pita wedges in a single layer on a baking sheet. Brush with the melted butter, then season with the sumac and some salt and pepper.
Bake, rotating the baking sheet halfway through, until browned and crispy, 8 to 10 minutes. Allow to cool on the baking sheet.
For the dip: Combine the picante peppers, olives and red and yellow bell peppers in a small bowl. Season with the oregano and toss with the olive oil and vinegar.
Spread half of the Baba Ghanoush on the bottom of a 10-inch square baking dish. Top with half of the pepper mixture. Top the pepper mixture with half of the Tzatziki. Repeat with the remaining Baba Ghanoush, pepper mixture and Tzatziki. Top with the tomatoes, feta and parsley. Sprinkle with the sumac and serve with the pita chips.
Preheat the oven or a grill to 400 degrees F.
Roast the eggplant, rotating once or twice during roasting, until soft, 30 to 45 minutes in the oven or 20 to 25 minutes on the grill. Transfer to a bowl, cover and let cool until cool enough to handle. Peel off the skin and discard.
Combine the eggplant, mayonnaise, feta, garlic and salt and pepper to taste in a food processor. Blend, while streaming in the olive oil, until pureed and smooth. Transfer to a bowl and refrigerate.
Combine the yogurt, cucumber, dill, mint, lemon juice and salt in a bowl and refrigerate until serving time.