I was successfully able to calculate phi, psi, omega values for proteins, given cartesian coordinates, where

phi: C-N-CA-C
psi: N-CA-C-N
omega: CA-C-N-CA

Now I would like to calculate chi angles for the side chains, also given cartesian coordinates, where

X1 = N-Ca-Cb-x
X2 = Ca-Cb-x-x

etc. where x can be Ca/b/c/d/e/f/g/ (any carbon-with-a-subscript).... or N (if I am not mistaken)

My first question is: Is that definition correct? If so, I believe it should be quite simple because (I think) it would be the same application for what I did for phi, psi, omega values, where I was given four cartesian coordinates per angle.

My second question is: I notice in the .pdb file, there are something carbons with the same subscript. What do in that case? For instance, the following case has CG1 and CG2:

ATOM     96  N   ILE A   6       1.201  -4.204   1.943  1.00  0.11           N 
ATOM     97  CA  ILE A   6       2.338  -5.105   2.255  1.00  0.13           C 
ATOM    100  CB  ILE A   6       2.067  -6.500   1.693  1.00  0.16           C 
ATOM    101  CG1 ILE A   6       0.952  -7.157   2.521  1.00  0.30           C 
ATOM    102  CG2 ILE A   6       3.348  -7.336   1.800  1.00  0.36           C 
ATOM    103  CD1 ILE A   6       0.238  -8.228   1.683  1.00  0.33           C 
ATOM    115  N   LEU A   7       4.435  -3.938   2.439  1.00  0.11           N 
ATOM    116  CA  LEU A   7       5.682  -3.321   1.900  1.00  0.12

Thank you