Determine the points of intersection between the curves in polar coordinates: $$ \left\{\begin{array}{l}r=3\\r=4\sin(3\theta)\\r=-\dfrac{1}{\sin(\theta)}\end{array}\right. $$
understand that I have to solve the systems of corresponding equations, but it generates a single value, I do not know how to generate the following points. And well, it is clear that I could do it by symmetry but formally / analytically can it be determined?
and one more question, to solve this integral $$\int\sqrt{12\cos(3\theta)+16\sin^{2}(3\theta)}d\theta$$ to use the Weierstrass substitution would be adequate?
HINT :
Draw the three curves and see the intersection points.
Computing the coordinates of each one is for you.