Let the side length of a small square be b and the side length of a large square be a,

Because: 4* triangle area+small square area = large square area.

The area of a right triangle is twice that of a small square.

So 4 * 2b 2+b 2 = 9b 2 = a 2.

So b=a/3.

AC=AB+BC=cosθ*a=sinθ*a+a/3

So cosθ-sinθ= 1/3 and (cos θ) 2+(sin θ) 2 = 1,

Sin2θ=8/9, because θ is an acute angle, and cos2θ= radical sign (65438+0 square of sin2θ) = (radical sign 17)/9.

sin^2θ-cos^2θ=？ -cos2θ=？ -(root number 17)/9