argument of a lacunary sum of roots of unity

Question

Let $q>4$ and $t< \sqrt{q}$ be integers. Determine the set $\{j_1,...,j_t\}$ of integers $0 \leq j_i <q-1$ such that $\arg(\sum_{i=0}^t e^{2i\pi\frac{j_i}{q}} ) \in [0,\pi[$.