Solution (source code)

= Solution

With
$$
Y=(Z_1,Z_2,Z_3,Z_4-2\pi)^T,\qquad
\theta=(\theta_1,\theta_2,\theta_3)^T,
$$
the model has
$$
\boxed{
X=\begin{pmatrix}
1&0&0\\0&1&0\\0&0&1\\-1&-1&-1
\end{pmatrix},\qquad
Y=X\theta+\varepsilon.}
$$