Let $f\left(x\right)=$  minimum  $(\cos x,\frac{1}{2},\left\{\sin x\right\}),0<x<2\pi .$  Let $x=x_i,i=1,2,3,\mathrm{...}n$  be the points where $f\left(x\right)$  is non-differentiable if $\sum _{i=1}^n{x}_i=\frac{\lambda \pi }{6}$  then value of $\lambda$ is
[Note: $\left\{k\right\}$  denotes the fractional part function of $k$ ]