find the inverse kinematics for a 6dof articulated robot

Question

I am working on a project to control a 6-axis robot and have successfully implemented the inverse kinematics for the first three joints. However, I am now stuck on how to solve for the inverse kinematics of the last three joints. I have the rotation (R1) and the position of the end of the end efecter and the rotation (R0) and the position of position a (see in the kinematic diagramm) kinematic diagramm denavit hartenberg table But I cant find the angles of the last three joints (j4, j5, j6).

I have tried multiple things like:

result = np.linalg.inv(R0) @ R1

    j4 = atan(sqrt(1-result[2, 2]**2)/result[2, 2])
    if sin(j4) > 0:
        j3 = atan2(result[0, 2], result[1, 2])
        j5 = atan2(result[2, 0], -result[2, 1])
    else:
        j3 = atan2(-result[0, 2], -result[1, 2])
        j4 = atan2(result[2, 2], sqrt(result[0, 2]+result[1, 2]))
        j5 = atan2(result[2, 0], -result[2, 1])

but it just does not give me the right angles to complete the inverse kinematics. Thanks for helping me.