Is there any known (symbolic) method that solves a system of equations/inequalities that have trigonometric functions on the left-hand side of the system?

Ex) Find $x,y,\theta \in \mathbb{R}$ that satisfy

\begin{align} 2x + y + 3\cos(\theta) - 2\sin(\theta) \le& 0 \\\ x - y + 4\cos(\theta) + 2\sin(\theta) \le& 0 \end{align}