Think about the expansion, it is not small

Calculus Level 4

\[\large \displaystyle L=\lim_{n \to \infty} \sum_{k=1}^{n} \dfrac{n-k}{n^2} \cos\left(\dfrac{4k}{n}\right) \]

Find the value of \(\lfloor 1000L \rfloor\).

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