Unexpected loop area result

[ericangle]

The below S2AreaCalculator computes the area of a lat/lon rectangle centered at $(0,0)$ with latitude width $2D$ and longitude width $2T$, where $D$ and $T$ are in degrees.

I would expect the area of this rectangle on the unit sphere to be

$$ \frac{T \pi}{45} \sin\left(\frac{D \pi}{180}\right) $$

I ran with $D = 1$ and $T = 89$ using

mvn compile exec:java -Dexec.mainClass="S2AreaCalculator" -Dexec.args="1.0 89.0"

which output

Expected area: 0.10843829588275879
Calculated area: 3.141288020704622
Calculated area / Expected area: 28.968437719649494
Expected area as fraction of unit sphere: 0.008629245405101292
Calculated area as fraction of unit sphere: 0.24997575808524833

This suggests that a thin rectangle at the equator is 1/4 of the entire sphere.

Do I have an error in how I'm implementing this, am I interpreting the area of an S2Loop incorrectly?

If I run with $T = 1$, the ratio of the calculated to expected areas is 1.000101520576819.

import com.google.common.geometry.S2LatLng;
import com.google.common.geometry.S2Loop;
import java.util.Arrays;

public class S2AreaCalculator {
    public static void main(String[] args) {
        double D = Double.parseDouble(args[0]); // half latitude width
        double T = Double.parseDouble(args[1]); // half longitude width

        double expectedArea = Math.PI*(T/45.0)*Math.sin(D*Math.PI/180.0);
        double expectedAreaFraction = expectedArea/(4.0*Math.PI);

        S2Loop loop = new S2Loop(Arrays.asList(
            S2LatLng.fromDegrees(-D, -T).toPoint(),
            S2LatLng.fromDegrees(-D, T).toPoint(),
            S2LatLng.fromDegrees(D, T).toPoint(),
            S2LatLng.fromDegrees(D, -T).toPoint()
        ));

        System.out.println("Expected area: " + expectedArea);
        System.out.println("Calculated area: " + loop.getArea());
        System.out.println("Calculated area / Expected area: " + (loop.getArea()/expectedArea));
        System.out.println("Expected area as fraction of unit sphere: " + expectedAreaFraction);
        System.out.println("Calculated area as fraction of unit sphere: " + loop.getArea()/(4.0 * Math.PI));
    }
}