$\large 2018 \exp \left(\int_{0}^{2 \pi} \cot (x + 2018 - 2018i) \, dx \right) =\ ?$

**Notations:**

- $\exp (x) = e^x$, where $e\approx 2.718$ denotes the Euler's number.
- $i = \sqrt {-1}$ denotes the imaginary unit.

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