1. When D and G coincide, the diagonals of rectangular ABCD are perpendicular to each other, so ABCD is a square, and x=AB=BC=4.

2. It can be proved that the triangle AEF is similar to CEB, and FE/BE=AF/BC= 1/2.

So let EF=y, BE=2y, BF=3y.

It can be proved that the triangle AEF is similar to BAF, and AF/EF=BF/AF.

So 2/y=3y/2, you get: y squared =4/3.

It can be proved that the triangle ABE is similar to FBA, and AB/BE=BF/AB.

So x/2y=3y/x is: x square =6y square =6*4/3=8.

So x= root number 8=2 root number 2

It can be proved that the triangle CDF and BAF are congruent, and CF=BF=3y is obtained.

So sin∠ECF=EF/CF=y/3y= 1/3.