Place the yoghurt in a medium bowl. Grate the cucumber on a box grater on the largest grating side and squeeze it with your hands to remove most (but not all) of the liquid.
Add the grated cucumber to the yogurt. Add the sour cream, lemon juice, vinegar, dill, garlic, 2 teaspoons salt, and 1/2 teaspoon pepper and combine. Taste for seasonings.
To serve, artfully arrange salad plates with slices of feta, drizzle them with olive oil, and sprinkle with thyme leaves. Add the olives, pita triangles, and the tzatziki and serve cold or at room temperature.
For the Toasted Pita Triangles: Preheat the oven to 175°C.
Slice the pita bread into 8 triangles and place them on a sheet pan. Place the sheet pan in the oven and toast the bread for 10 minutes.