The value of $\cot\sum\limits_{n=1}^{23}\cot^{-1}\big(1+\sum\limits_{k=1}^n 2k\big)$ is

Question

$(a)\;\large\frac{23}{25}$$\qquad(b)\;\large\frac{25}{23}$$\qquad(c)\;\large\frac{23}{24}\qquad$$(d)\;\large\frac{24}{23}$