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The curves are  and .

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

General solution of  is , where is an integer.

If , then .

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 intersect points on the interval .

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

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

Area of the region that lies inside the both curves is . \ \