Generic nonlinear system

$$\begin{align*} \dot{x}_1 &= x_1 = x_1x_4 + \theta_1x_1^2 \theta_2x_3 + x_2u_1 + u_2 + u_3 \\ \dot{x}_2 &= x_2\cos{x_3} + \theta_3x_4 + u_1 + u_4 \\ \dot{x}_3 &= \sin{x_2} - x_3 \\ \dot{x}_4 &= x_3 - x_4 + x_1x_4 + \theta_1x_1^2 + (1 + x_2)u_1 + u_2 + u_3 \\ y_1 &= x_1 \\ y_2 &= x_2, \end{align*}$$

where $\theta_1 = 0.5$, $\theta_2 = 2$, and $\theta_3 = 1$ are unknown constant parameters.