The curves are  and .

First find out the points, where the two curves intersect.

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Graph two curves in polar - coordinate plane.

Graph :

We can observe from the graph that the two curves intersect at 8 points.

There are 8 intersects on the interval .

By symmetry area of the region that lies inside the both curves :

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Area of the region that lies inside the both curves is  square units.

Area of the region that lies inside the both curves is  square units.