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.