
  You want to solve this nonlinear system of equations :
       (with A, B, C  [0..2pi])
 
        a cos(A) + b cos(B) + c cos(C) = d
        e cos(A) + f cos(B) + g cos(C) = h
        i cos(A) + j cos(B) + k cos(C) = l

  If you write :

               cos(A) = x
               cos(B) = y
               cos(C) = z
    
  You can rewrite the system :

        a x + b y + c z = d
        e x + f y + g z = h
        i x + j y + k z = l

 Which is a linear system of equation in x, y, z.

 Suppose, the solution of the system is :

                    x = r
                    y = s
                    z = t 

 you can write
               cos(A) = r    if r = 1    A =  0   or A =  2pi 
               cos(B) = s    if s = 1/2  B = pi/3 or B =  5pi/3
               cos(C) = t    ...
 
 The good values for r, s, t are : -1, -1/2, 0, 1/2, 1.

 The other values are difficult to write with our numbers.