I am calculating some residue calculus stuff, where I need to know if the prescribed poles are inside the curve given above, namely $2\sin(2\theta)$ for $0\leq \theta<2\pi$. I actually need to know if these are $( e^{(\pi i)/4}, e^{(3\pi i)/4},e^{(5\pi i)/4},e^{(7\pi i)/4})$inside the curve or not?
I am actually very bad at graphing, any help will be much appreciated.