$(30$ points$)$ The mean camber line for a thin$-$airfoil with unit chord length $c=1$ is given by

$z(x)=a[(b-1)x^3-b{x}^2+x],x=\frac{1}{2}(1-cos)$

where $a,b$ are constants. Also,

$\frac{dz}{dx}=a[\frac{3}{8}(b-1)cos2+\frac{3-b}{2}cos+\frac{b-1}{8}]$

What is the value of $b$ when the angle of attack for zero lift is zero