The value of \(\displaystyle\cot\left\{\sum_{n=1}^{23}\cot^{-1}\left(1+\sum_{k=1}^{n}2k\right)\right\}\) is

1
\(\dfrac{23}{25}\)
2
\(\dfrac{25}{23}\)
3
\(\dfrac{23}{24}\)
4
\(\dfrac{24}{23}\)

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