# Calculating area bounded by polar curves

Find the area bounded by the following polar curves $$r<3|sin(2t)|$$

Well, I know that the formula used to calculate an area bounded by $$g(t) \le r \le f(t)$$ with $$\alpha \le t \le \beta$$ is $$A=\frac{1}{2} \int_{\alpha}^{\beta} [f(t)]^2 - [g(t)]^2 \,dt$$

So, $$g(t)=-3sin(2t)$$ and $$f(t)=3sin(2t)$$. And then I have to look for the intersections between $$g(t)$$ and $$f(t)$$ to find $$\alpha$$ and $$\beta$$. And after that? Because they intersect each other in more than one interval. And also, how can I find the intersection? Because I have problems with the $$(2t)$$ of $$sin(2t)$$.

$$A = 4 \int\limits_{\theta = 0}^{\pi/2} \int\limits_{r=0}^{|\sin (2 \theta)|} r\ dr\ d\theta = \frac{\pi}{8}$$