The value of $\frac{\sin 24°\cos 6°-\sin 6°\sin 66°}{\sin 21°\cos 39°-\cos 51°\sin 69°}$ is

If $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2-ax+b=0,$ then the value of ${\sin }^2(A+B)$ is

If $A+B=225°,$ then the value of $\left(\frac{\cot A}{1+\cot A}\right)·\left(\frac{\cot B}{1+\cot B}\right)$ is