Diamadarithmos: The Greek Sudoku

What is a Diamadarithmoi puzzle? Diamadarithmoi is the Greek word for the puzzle "Diamonds and Numbers". In this type of puzzle you must put the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 into the following diamonds in the way that each cell contains only one digit. Add like SUDOKU each digit must be used just once!!! How you can solve Diamadarithmoi? You must create the original four numbers A, B, C and D. For your help the addition of these numbers (A, B, C and D) is given, for your help, with many ways. Also you must remember that each English letter of this puzzle is coded with a Greek one, with the following formula.