2D mouse angle in 360 degrees?

Here is some code that implements three different ways to find that angle. Note way #1 and way #2 assume the camera is looking along the Z axis. If you are doing a top view by looking down the Y axis, you will need to make the appropriate changes. Take this script and attach it to an empty game object. Drag an object into the scene for goPlayer.

 public class FindAngle : MonoBehaviour {
      public GameObject goPlayer;
     
     void Update() {
     
     Vector3 v3Pos;
     float fAngle;
     
     if (Input.GetMouseButtonDown(0)) {
             // Project the mouse point into world space at
             //   at the distance of the player.
             v3Pos = Input.mousePosition;
             v3Pos.z = (goPlayer.transform.position.z - Camera.main.transform.position.z);
             v3Pos = Camera.main.ScreenToWorldPoint(v3Pos);
             v3Pos = v3Pos - goPlayer.transform.position;
             fAngle = Mathf.Atan2 (v3Pos.y, v3Pos.x) * Mathf.Rad2Deg;
             if (fAngle < 0.0f) fAngle += 360.0f;
             Debug.Log ("1) "+fAngle);
                 
             // Raycast against a mathematical plane in world space
             Plane plane = new Plane(Vector3.forward, goPlayer.transform.position);
             Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition);
             float fDist;
             plane.Raycast(ray, out fDist);
             v3Pos = ray.GetPoint (fDist);
             v3Pos = v3Pos - goPlayer.transform.position;
             fAngle = Mathf.Atan2 (v3Pos.y, v3Pos.x) * Mathf.Rad2Deg;
             if (fAngle < 0.0f) fAngle += 360.0f;
             Debug.Log ("2) "+fAngle);
                 
             //Convert the player to Screen coordinates
             v3Pos = Camera.main.WorldToScreenPoint(goPlayer.transform.position);
             v3Pos = Input.mousePosition - v3Pos;
             fAngle = Mathf.Atan2 (v3Pos.y, v3Pos.x)* Mathf.Rad2Deg;
             if (fAngle < 0.0f) fAngle += 360.0f;
             Debug.Log ("3) "+fAngle);    
         }
     }
 }