Suppose lim_x → 0 (F (x))/x^3 exists and is equal to L, where F (x)= |a + sin x/2, - b cos x, 0; - b cos x, 0, a + sin x/2; 0, a + sin x/2, - b cos…

Suppose $\displaystyle \lim _{x \rightarrow 0} \frac{\mathrm{~F}(x)}{x^3}$ exists and is equal to L , where $$\mathrm{F}(x)=\left|\begin{array}{ccc} \mathrm{a}+\sin \frac{x}{2} & -\mathrm{b} \cos x & 0 \\ -\mathrm{b} \cos x & 0 & \mathrm{a}+\sin \frac{x}{2} \\ 0 & \mathrm{a}+\sin \frac{x}{2} & -\mathrm{b} \cos x \end{array}\right| . $$ Then, -$\displaystyle 112$ L is equal to \_\_\_\_.