AMC 12 2024b Problem 11

Let $x_{n} = \sin^2(n^\circ)$. What is the mean of $x_{1}, x_{2}, x_{3}, \cdots, x_{90}$?

$\textbf{(A) }\frac{11}{45} \textbf{(B) }\frac{22}{45} \textbf{(C) }\frac{89}{180} \textbf{(D) }\frac{1}{2} \textbf{(E) }\frac{91}{180}$