A puzzle by way of the Mathematics Stack Exchange and/or Quora. (Know the original source? Tell me!)
$$\text{shaded area} \;=\; \text{???}$$
SPOILERS
$$\begin{align}3u + v &= 3u \;+\; |OPST| \;-\; |\text{sector}\;OPT| \\[6pt]
&= 3u \;+\; \frac{3}{5}\;|\triangle SRT| \;-\; |\text{sector}\;OPT| \\[6pt]
&= 3\cdot \frac{1}{4}r^2\left( 4-\pi \right) \;+\;\frac{3}{5}\cdot r^2 \;-\; \frac{1}{2}r^2 \cdot 2\theta
\end{align}$$
$$\text{shaded area} \;=\; r^2\left(\;\frac{18}{5} \;-\; \frac{3}{4}\pi \;-\; \operatorname{atan}\frac{1}{2}\;\right)$$