\( S=3 \sum_{n=1}^{\infty}\left\{\frac{1}{\pi} \sum_{K=1}^{\infty} \cot ^{-1}\left(1+2 \sqrt{\su...

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\( S=3 \sum_{n=1}^{\infty}\left\{\frac{1}{\pi} \sum_{K=1}^{\infty} \cot ^{-1}\left(1+2 \sqrt{\sum_{r=1}^{K} r^{3}}\right)\right\}^{n} \), then \( \mathrm{S} \) cant be
(a) 2021
(b) 2022
(c) 2023
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