$C \rightarrow -C.$

Let $C: \left[ 0, 2 \pi \right) \rightarrow \mathbb{R^2}$ represent the curve parametrized in the following way:

$x(\theta) = \cos(\theta), \;\; y(\theta) = \sin(\theta), \;\; \theta \in \left[ 0, 2 \pi \right)$

We want to find a linear dependence of $\theta$ on some parameter $0 \leq t < 2 \pi$ that takes $C$ to $-C.$ If that dependence is of the form

$\theta(t) = \frac{\pi}{2} b - at,$

where $a$ and $b$ are the lowest possible positive numbers. Find $\theta(-3 \pi /2).$