Limits Continuity And Differentiability

Let $[x]$ denote the greatest integer less than or equal to $x$ and $k \geq 2$ be an integer. Then

\(\mathop {Lt}\limits_{x \to k} \frac{\sin \left(2 \pi\left([x]-\left[\frac{x}{k}\right]\right)-x\right)+\sin k}{x-k}=\)