Custom LookAt and what's the math behind it

I've been trying to understand more the math (trigonometry and linear algebra) be$$anonymous$$nd the transform.LookAt() function. I followed a tutorial and tried to modify it to fit my needs, but I haven't succeeded so far.

I'm trying to ac$$anonymous$$eve a camera (in 3d space) that is following a player with a custom offset but at the same time the user can zoom the camera in and out all w$$anonymous$$le still having that Vector3 offset. I'm also locking the other axes, and just only want to apply the rotation to the X axis. The problem with my script is that the angle seems to be clamped between 45° and 90° degrees. I t$$anonymous$$nk I'm probably missing somet$$anonymous$$ng. from the code:

 private void LookAt(Transform t) {
     Vector3 forward = _camPos - (t.position + new Vector3(0, t.GetComponent<CapsuleCollider>().height / 2, 0));
     Debug.DrawRay(forward, -forward, Color.blue);
     Vector3 right = Vector3.Cross(target.up, forward);
     Debug.DrawRay(forward, right, Color.magenta);
     Vector3 newUp = Vector3.Cross(Vector3.forward, right);
     Debug.DrawRay(forward, newUp, Color.yellow);
 
     float angle = Mathf.Atan2(forward.magnitude, newUp.magnitude) * Mathf.Rad2Deg;
 
     mainCam.transform.rotation = Quaternion.Euler(angle, 0, 0);
 }

• My code first get's the forward vector (hypotenuse in a right triangle) from the camera to the target. Side note here, that t$$anonymous$$s gives the opposite direction, but it doesn't matter because

• it then calculates the "right" vector by having the cross product of the forward vector and the target's up vector

• then it calculates the "newUp" vector (opposite in a right triangle)

• calculates the X rotation by using Arcus tangent w$$anonymous$$ch is the ratio between the hpyotenuse/opposite
  
  As you can see, the vector calculations are right like on the screenshot
  
  

• blue forward vector

• magenta right vector

• yellow newUp vector

Still, the camera is only focusing on the character properly when I decrease the zoom rate, a.k.a moving the camera closer to it:

What am I missing? Help greatly be appreciated :)