Drain any excess water from the feta and ricotta, then mix together with the Pecorino and eggs. Season to taste. Stir together the butter and olive oil. Unwrap the filo pastry, keeping any pastry you are not using covered with a damp (but not wet) tea towel.
Cut each pastry sheet into thirds lengthways and brush all over with the butter mixture. Place a heaped spoonful of the cheese mixture at one end of a strip of pastry. Fold one corner of the pastry diagonally over the filling to meet the other side, then continue to fold all the way down the strip to create a triangular parcel. Repeat with the remaining pastry and ingredients.
Place the parcels on a lightly greased baking sheet, brush over again with the butter and oil and bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 12 minutes or until golden and crisp. Serve warm from the oven.