تابع با ضابطه $f\left( x \right)=\left\{ \begin{matrix}
ax+\sin \frac{\pi }{x}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{۱}{۲}\le x\lt ۲ \\
-۱\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=۲ \\
b{{\cos }^{۲}}\left( \frac{\pi }{۲x} \right)-a\,\,\,\,\,\,\,\,\,\,\,۲\lt x\lt ۴ \\
\end{matrix} \right.$ در نقطه $x=۲$ پیوسته است. $b$ کدام است؟