For some a, b, let f(x)= |a +(sin x)/x, 1, b; a, 1+(sin x)/x, b; a, 1, b +(sin x)/x|, x ≠ 0, lim_x → 0 f(x)=λ+μ a +ν b. Then (λ+μ+ν)^2 is equal to:

For some $\displaystyle \mathrm{a}, \mathrm{b}$, let $\displaystyle f(x)=\left|\begin{array}{ccc}\mathrm{a}+\frac{\sin x}{x} & 1 & \mathrm{~b} \\ \mathrm{a} & 1+\frac{\sin x}{x} & \mathrm{~b} \\ \mathrm{a} & 1 & \mathrm{~b}+\frac{\sin x}{x}\end{array}\right|, x \neq 0, \lim _{x \rightarrow 0} f(x)=\lambda+\mu \mathrm{a}+\nu \mathrm{b}$. Then $\displaystyle (\lambda+\mu+\nu)^2$ is equal to :