Preheat oven to 350 F. Lightly grease 2 large baking sheets.
In a large bowl, using a fork, crumble the feta cheese into small pea-sized pieces.
Add the remaining cheeses and mix well.
Add the eggs and combine with a spoon or spatula until mixture is loose but not too thin. It should be slightly lumpy.
Carefully remove the phyllo roll from the plastic sleeve. Most packages come in 12- x 18-inch sheets when opened fully. Using a scissor or sharp knife, cut the sheets in half to make two stacks of 9- x 12-inch sheets. To prevent drying, cover one stack with waxed paper and a damp paper towel while working with the other.
Remove a sheet from the stack and place it in front of you vertically. Using a pastry brush, butter the surface of the sheet taking care not to tear it.
Drop a tablespoon of filling in the center of the sheet horizontally about 1/2-inch up from the bottom edge.
Fold the right edge two-thirds over, covering the filling.
Repeat with the left side.
You should have a long strip about 3 inches wide in front of you, with a bulge of filling at the bottom. Brush the strip with more melted butter.
Fold the bottom corner up and over the filling bulge to the opposite edge, creating a triangle.
Fold the bottom edge of the triangle up to the opposite side, like folding a flag.
Continuing folding the triangle up and over to the opposite side each time, until you reach the end of the strip.
Place the triangle on the greased baking sheet. Repeat with the remaining sheets and filling.
Brush the triangles with melted butter. Bake until golden and flaky, 20 to 25 minutes.
Allow triangles to cool for 5 to 10 minutes before serving.
