2023 AMC 12A Problem 25

There is a unique sequence of integers a_1, a_2, \cdots a_{2023} such that \[ \begin{gathered} \tan 2023x\\ {}=\tiny\dfrac{a_1\tan x+a_3\tan^3 x+a_5\tan^5 x+\cdots+a_{2023}\tan^{2023}x}{1+a_2\tan^2 x+a_4\tan^4 x\cdots+a_{2022}\tan^{2022}x} \end{gathered} \] whenever \tan 2023x is defined. What is a_{2023}?

\textbf{(A)} -2023 \qquad \textbf{(B)} -2022 \qquad \textbf{(C)} -1 \qquad \textbf{(D)} 1 \qquad \textbf{(E)} 2023

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.