Find the area lying inside the circle $r=a \sin \theta$ and outside the cardioid $r=a(1-\cos \theta)$.

Question

I calculated this area to be:

$$\int_{0}^{\pi/2} \int_{a(1- \cos\theta)}^{a \sin\theta} r \ \mathrm dr\ \mathrm d \theta=a^2\int_{0}^{\pi/2} \cos\theta - \cos^2\theta \ \mathrm d \theta= a^2(1-\frac{\pi}{4}).$$

Just want to verify that my formulation and answer are correct since I do not have the correct answer myself.