The value of \( \cot \left\{\sum_{n=1}^{23} \cot ^{-1}\left(1+\sum_...

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The value of \( \cot \left\{\sum_{n=1}^{23} \cot ^{-1}\left(1+\sum_{k=1}^{n} 2 k\right)\right\} \) is
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(a) \( \frac{23}{25} \)
(b) \( \frac{25}{23} \)
(c) \( \frac{23}{24} \)
(d) \( \frac{24}{23} \)
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