Question: How can I make the region below colored

I did two polar plots as you see and wanted to color the region between them.

> with(plots);
> a1 := polarplot(1, t = 0 .. 6*Pi*(1/3), thickness = 2, filled = true, color = black);
> a2 := polarplot(2*cos(t), t = 0 .. 6*Pi*(1/3), thickness = 2);
> a3 := polarplot(2*cos(t), t = -(1/3)*Pi .. (1/3)*Pi, filled = true, thickness = 2);
> display(a1, a2, a3);

The program makes the region colored red but there is an overlapping part which I don't want it. How could I have just the red colored region? The region looks like a crescent. Thanks.

 

 

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