Help with an identity involving PolyLog and Logs.

Question

I am plotting the following expression on Mathematica $$ \Im\left[-96 \text{Li}_3\left(e^{-i t}\right)-48 t^2 \log \left(1-e^{-i t}\right)\right]-96 \Re\left[t \text{Li}_2\left(e^{-i t}\right)\right]-8 t^3) $$ over a range of $t \in (0,2\pi)$, and find it to be of the order of $10^{-17}$, and very noisy. Often this happens because the actual value is zero, so I was wondering if such a thing can be shown using some identities involving Clausen functions ? I tried looking at few identities in wiki and wolfram but was not of much help.