A calculus problem by Navdeep Nainwal

Calculus Level pending

Integration of [cot(x)], with respect to dx from limits 0 to pie and here [ ] represents greatest integer function.

\[\large \int_0^\pi \lfloor \cot x \rfloor \ dx = \ ? \]

Notation: \(\lfloor \cdot \rfloor\) denotes the floor function.

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