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

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

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