# Problem with calculating a winding number

I have a problem with calculating the winding number $n\left ( \gamma ,\frac{1}{3} \right )$ of the curve $\gamma :\left [ 0,2\pi \right ]\rightarrow \mathbb{C}, t \mapsto \sin(2t)+i\sin(3t)$.

According to the formula $\frac{1}{2\pi i}\int_{0}^{2\pi }\frac{\gamma{}' {(t)}}{\gamma (t)-\frac{1}{3}}dt$ i get a strange integral to calculate: $\frac{1}{2\pi i}\int_{0}^{2\pi }\frac{2\cos(2t)+3i\cos(3t)}{\sin(2t)+i\sin(3t)-\frac{1}{3}}dt$...

I don't know how to move on...there should be another way how to do it with plotting the curve around $\frac{1}{3}$, but i don't know how to do it and can't find software for this. Can anybody help me, please? Thank you in advance!

Notice that as you trace around the curve, it doesn't wind around the point $z=\frac{1}{3}$, so the winding number is $0$.