Can you simplify $$\large\operatorname{Li_3} \frac{1}{3} $$
It might be impotant to note that $$\operatorname{Li_3}\frac{1}{2}=\frac{7\zeta(3)}{8}+\frac{\log^3 2}{6}-\frac{\pi^2\log 2}{12}$$
But I do not know enough properties of Polylogarithms to solve it.