The points of intersection of the cardioid $r=1+\sin(\theta)$ and the spiral loop $r=2\theta,\; -\pi/2 \le \theta \le \pi/2,$ can't be found exactly. Instead, we can use a graphing device to find that the approximate values of $\theta$ at which these curves intersect are $\theta \approx 0.89$ and $\theta \approx 2.25.$ Use these values to estimate the area that lies inside both curves. Make sure your answer is correct (based on the estimates given above) to three decimal places.

Area $\approx$