sequences and series - Why is $sum_{n=1}^infty frac{(-1)^{n+1}sin(n)}{n}$ equal to $frac{1}{2}$?

I was randomly playing around on Desmos, and I realized that this series seems to evidently converge to $\frac{1}{2}$. Is there any reason why this converges to such a nice number?

Please note that I am in high school, so if this is requires an incredibly complex solution I may not understand it (but if it would be of value to others, go ahead)