Let $w$ and $z$ be complex numbers such that $|w| = 1$ and $|z| = 10$. Let $\theta = \arg \left(\frac{w-z}{z}\right)$. Find the maximum possible value of $\tan^2 \theta.$  (Note that $\arg(w),$ for $w \neq 0,$ denotes the measure of the angle that the ray from 0 to $w$ makes with the positive real axis in the complex plane.)
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $w$ and $z$ be complex numbers such that $|w| = 1$ and $|z| = 10$. Let $\theta = \arg \left(\frac{w-z}{z}\right)$. Find the maximum possible value of $\tan^2 \theta.$  (Note that $\arg(w),$ for $w \neq 0,$ denotes the measure of the angle that the ray from 0 to $w$ makes with the positive real axis in the complex plane.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{99}
Let $w$ and $z$ be complex numbers such that $|w| = 1$ and $|z| = 10$. Let $\theta = \arg \left(\frac{w-z}{z}\right)$. Find the maximum possible value of $\tan^2 \theta.$  (Note that $\arg(w),$ for $w \neq 0,$ denotes the measure of the angle that the ray from 0 to $w$ makes with the positive real axis in the complex plane.)
train