Determine the value of A² + B² + C² + D², given that the following set of four equations are satisfied simultaneously:

  
   A2       B2       C2       D2
 ------ + ------ + ------ + ------ = 1
  22-1    22-32    22-52     22-72

   A2       B2       C2       D2
 ------ + ------ + ------ + ------ = 1
  42-1    42-32    42-52     42-72

   A2       B2       C2       D2
 ------ + ------ + ------ + ------ = 1
  62-1    62-32    62-52     62-72
   A2       B2       C2       D2
 ------ + ------ + ------ + ------ = 1
  82-1    82-32    82-52     82-72