Can anyone help me solve this problem?

Can anyone help me solve this problem?

It probably involves trigonometry but not exclusively....

I have three known world-space xyz points located on a plane. All three of these points are visible to the camera.

The cameras frustum is known and the locations in the cameras pixel space of each of the three points of

the plane are also known.

From this information is it possible to calculate the transformation matrix of the plane? I can only think of an

iterative method that doesn't seem very robust.

Thanks in advance!