If your viewpoint changes, do the angles between the 3D edges of the box change?
No. Changing your viewpoint does not change the 3D objects. But the 2D picture changes.
The angle between two vectors in 3D depends on their relation to each other (and does not depend on your viewpoint, or the coordinate frame you are using). Of course, when a 2D picture shows a 3D scene the angles in the picture very much depend on the viewpoint.
In the previous chapter you saw a formula for the angle θ between two unit vectors:
au · bu = cosθ
Apply this formula to the two unit vectors parallel to the x axis and y axis: (1,0,0)T and (0,1,0)T.