2025 AMC 12B 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 \qquad \textbf{(B)} \sqrt{2} - 1 \qquad \textbf{(C)} 2 - \sqrt{2} \qquad \textbf{(D)} \dfrac{\sqrt{2}}{2} \qquad \textbf{(E)} 3 - \sqrt{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.