Two sheets of paper

The European standard paper size, A4, is a rectangle where the ratio of the lengths of sides is sqrt(2) : 1.

Let there be two such papers, ABCD and A'B'C'D' where AB and A'B' are the shorter sides. The papers are place so that the latter exactly covers the former. Then the latter is rotated a few degrees clockwise so that

C' is on the side CD
D' is on the side AD
B is on the side A'D'.

How many degrees is the latter paper rotated to accomplish that?
How large a % of the area of ABCD is visible as three triangles around A'B'C'D'?

Originally posted by talzamir
The European standard paper size, A4, is a rectangle where the ratio of the lengths of sides is sqrt(2) : 1.

Let there be two such papers, ABCD and A'B'C'D' where AB and A'B' are the shorter sides. The papers are place so that the latter exactly covers the former. Then the latter is rotated a few degrees clockwise so that

C' is on the side CD
D' is ...[text shortened]...
How large a % of the area of ABCD is visible as three triangles around A'B'C'D'?

I get ~62.0 degrees rotation; and ~38.7% area.