Mismatch in Angles After Z-matrix to XYZ Conversion in zmat_to_xyz

Describe the bug
When converting a Z-matrix to XYZ coordinates using the zmat_to_xyz function, the angle A_8_2_1 is incorrectly calculated. It is defined as 77.4° in the Z-matrix, but after conversion and visualization in GaussView, it is shown as 51.93824°. All other parameters appear to be converted correctly.
This is just one example, but I’m encountering the same issue with other molecules as well, consistently with the angle A_8_2_1.

How to reproduce

zmat = {
    'symbols': ('C', 'O', 'C', 'O', 'H', 'H', 'H', 'H', 'O', 'H', 'H'),
    'coords': (
        (None, None, None),
        ('R_1_0', None, None),
        ('R_2_1', 'A_2_1_0', None),
        ('R_3_2', 'A_3_2_1', 'D_3_2_1_0'),
        ('R_4_0', 'A_4_0_1', 'D_4_0_1_3'),
        ('R_5|6_0|0', 'A_5|6_0|0_1|1', 'D_5_0_1_4'),
        ('R_5|6_0|0', 'A_5|6_0|0_1|1', 'D_6_0_1_5'),
        ('R_7_2', 'A_7_2_3', 'D_7_2_3_6'),
        ('R_8_2', 'A_8_2_1', 'D_8_2_7_3'),
        ('R_9_8', 'A_9_8_2', 'D_9_8_2_1'),
        ('R_10_8', 'A_10_8_9', 'D_10_8_9_2')
    ),
    'vars': {
        'R_1_0': 1.4279748215793069, 'R_2_1': 1.7627308829567612, 'A_2_1_0': 113.78880933352458,
        'R_3_2': 1.220223245519294, 'A_3_2_1': 126.68953118378808, 'D_3_2_1_0': 6.273929367455621e-06,
        'R_4_0': 1.093536138062114, 'A_4_0_1': 108.0618680369275, 'D_4_0_1_3': 61.484528505772055,
        'R_7_2': 1.1010626883230803, 'A_7_2_3': 124.35232167955662, 'D_7_2_3_6': 199.80067229824692,
        'R_8_2': 1.85, 'A_8_2_1': 77.4, 'D_8_2_7_3': 140,
        'R_9_8': 1.21, 'A_9_8_2': 70, 'D_9_8_2_1': 1.64,
        'R_10_8': 0.97, 'A_10_8_9': 111, 'D_10_8_9_2': 103
    },
    'map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10}
}

xyz = zmat_to_xyz(zmat)
print(xyz)

To reproduce the issue, convert the Z-matrix using the zmat_to_xyz function. Next, visualize the resulting XYZ coordinates in GaussView and examine the geometric structure. Compare the angle A_8_2_1 in the XYZ output to its defined value in the Z-matrix (77.4°) and note the discrepancy.

Expected behavior
The angle A_8_2_1 should match its defined value in the Z-matrix (77.4°).

Additional context
Gaussian successfully computes the correct angle using the same Z-matrix, so the discrepancy appears to be specific to ARC’s zmat_to_xyz function.
- Observed XYZ from zmat_to_xyz:

C          -0.25870627  -0.85853197  -1.53345513
O          -0.25870627  -0.85853197  -0.10548031
C          -0.25870627   0.75443460   0.60554643
O          -0.25870638   1.81623563   0.00427832
H           0.65482121  -0.36220752  -1.87249919
H          -0.25870630  -1.88367885  -1.91708716
H          -1.11876827  -0.30066148  -1.91708716
H          -0.29397484   0.66137562   1.70210249
O           0.91829111  -0.63533633   0.93068322
H           0.10796546  -0.96617019   0.09520653
H           0.70717317  -1.02539152   1.79334547

- Observed XYZ from Gaussian:

C                  0.00000000    0.00000000    0.00000000
O                  0.00000000    0.00000000    1.42800000
C                  1.61293842    0.00000000    2.13901402
O                  2.67471880    0.00000000    1.53775661
H                  0.49630837   -0.91349690   -0.33903344
H                 -1.02516826   -0.00000000   -0.38363940
H                  0.55788139    0.86008042   -0.38363940
H                  1.51987759    0.03526445    3.23560752
O                  0.68578419    1.16051832    3.24177521
H                 -0.05359017    0.71661428    2.39302628
H                  0.95208240    2.06894661    3.03024906