△ $\mathit{ABC}$的内角 $\mathit{A\hspace{0.33em}}，\mathit{\hspace{0.33em}\hspace{0.33em}B\hspace{0.33em}}，\mathit{\hspace{0.33em}\hspace{0.33em}C}$的对边分别为 $\mathit{a\hspace{0.33em}}，\mathit{\hspace{0.33em}\hspace{0.33em}b\hspace{0.33em}}，\mathit{\hspace{0.33em}\hspace{0.33em}c}$，已知 $b\text{sin}C+c\text{sin}B=4a\text{sin}B\text{sin}C$， $b^2+c^2-a^2=8$，则△ $\mathit{ABC}$的面积为________．