AMC 12 2025b Problem 16

An analog clock starts at midnight and runs for $2025$ minutes before stopping. What is the tangent of the acute angle between the hour hand and the minute hand when the clock stops?

$\textbf{(A) } 0 \textbf{(B) } \sqrt{2}-1 \textbf{(C) } 2-\sqrt{2} \textbf{(D) } \frac{\sqrt{2}}{2} \textbf{(E) } 3-\sqrt{2}$