There is a unique sequence of integers $a_1,a_2,\dots ,a_{2025}$ such that

$\tan 2025x=\frac{a_1\tan x+a_3{\tan }^{3}x+a_5{\tan }^{5}x+\cdots +a_{2025}{\tan }^{2025}x}{1+a_2{\tan }^{2}x+a_4{\tan }^{4}x+\cdots +a_{2024}{\tan }^{2024}x}$

whenever $\tan 2025x$ is defined. What is $a_{2025}$?