There is a unique sequence of integers a_{1}, a_{2}, a_{3}, \ldots, a_{2023} such that
\tan 2023 x=\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}
whenever \tan 2023 x is defined. What is a_{2023}?
Answer Choices
A. -2023
B. -2022
C. -1
D. 1
E. 2023