Let  $f:(-\frac{\pi }{4},\frac{\pi }{4})\to R$   be defined as $f\left(x\right)=\{\begin{array}{l}{(1+\left|\sin x\right|)}^{\frac{3a}{\left|\sin x\right|}}\text{ ; }if-\frac{\pi }{4}<x<0\\ b\text{ ; }ifx=0\\ e^{\frac{\cot 4x}{\cot 2x}};if0<x<\frac{\pi }{4}\end{array}$ . If  $f\left(x\right)$  is continuous at  $x=0,$  then the value of  $6a+b^2=$ _____