The function cv2.solvePnP of OpenCV in Python keep return vectors that far from right.

here is the code:

    import numpy as np
    import cv2

    k = np.eye(3)  # I added this here for the code to run. I use some matrix from a file. it is not suppose to change the results, since we use the same matrix for the creating the data and for     cv2.solvePnP

    # create 3d points in homogenous coordinates
    points_3d = np.array([
        [1.0, 1.0, 8.0, 1.0],
        [1.0, -1.0, 7.9, 1.0],
        [-1.0, 1.0, 8.0, 1.0],
        [-1.0, -1.0, 9.0, 1.0],
    ]).T

    # create trivial transformation that rotate by pi/8 around the Z axis(the camera line of sight)
    transformation = np.array([
        [np.cos(np.pi/8), -np.sin(np.pi/8), 0.0, 0.0],
        [np.sin(np.pi/8), np.cos(np.pi/8), 0.0, 0.0],
        [0.0, 0.0, 1.0, 0.0],
    ])
    
    # project the 3D points to the camera as pixels
    pixels_2d = k @ transformation @ points_3d
    pixels_2d /= pixels_2d[2, :]
    pixels_2d = pixels_2d[:2, :]

    # fix the format of the array according to OpenCV docs
    pixels_2d = np.ascontiguousarray(pixels_2d.reshape((4, 1, 2)))
    points_3d = np.ascontiguousarray(points_3d[:3, :].reshape((4, 3)))

    # call cv2.solvePnP
    _, r, t = cv2.solvePnP(points_3d, pixels_2d, k, None, flags=cv2.SOLVEPNP_P3P)

    # The expected results suppose to be very close to the rotation and translating that create the data.

    r, _ = cv2.Rodrigues(r)

    print(f'rotation matrix R=n{r}ntranslation vector t=n{t}')

    >>>rotation matrix R=
    [[ 0.33196511 -0.65448479 -0.67930025]
     [ 0.73226038  0.63276397 -0.25180249]
     [ 0.59463762 -0.41383501  0.68930884]]
    translation vector t=
    [[-0.10543042]
     [ 1.17869639]
     [ 4.22398241]]

I tried to change the argument I pass to the function cv2.solvePnP with no success.
In most cases the function returns Error.

Python 3.11.5
opencv-python 4.9.0.80
numpy 1.26.4