What is the maximum modulus of a dot product over the distinguished boundary of the standard polydisc?

Question

Let $\mathbf{a} \in \mathbb{C}^2$.

For each $\mathbf{c} = (c_1, c_2)\in \mathbb{C}^2$, what is the maximum value of $$|\mathbf{c} \cdot \mathbf{z}|= |c_1 \exp(-it_1) + c_2 \exp(-it_2)|$$ as $\mathbf{z}$ ranges over all vectors $(\exp(it_1), \exp(it_2)) \in S^1 \times S^1$ perpendicular to $\mathbf{a}$?