Q: Find the area inside the region bounded by both r = sin theta and r = sin (2 theta)

I set the integral to.........

2[1/2{(sin 2x)^2 dx - 1/2{(sin2x)^2 - (sinx)^2 dx]

Notes: For efficiency, I used x for theta. Also, the limits of integration for each integral are from 0 to pi/3.

But my book says this, which doesn't make sense -

2[1/2{(sinx)^2 dx + 1/2{(sin2x)^2 dx]

Limits of integration for first integral: from 0 to pi/3

Limits of integration for second integral: from pi/3 to pi/2

Help please!

Cheers!