I am trying to tackle the following problem:

Let $A_{f},A_{g} \in \R^{3 \times 3}$ be symmetric matrices and let $f: [-\pi,\pi)^{2} \to \mathbb{R}$ and $g: [-\pi,\pi)^{2} \to \mathbb{R}$ that map $(\theta_{1},\theta_{2})$ to $(\cos\theta_{1}, \sin\theta_{1}, 1)A_{f}\begin{pmatrix}\cos\theta_{2}\\ \sin\theta_{2}\\ 1\end{pmatrix}$ and $(\cos\theta_{1}, \sin\theta_{1}, 1)A_{g}\begin{pmatrix}\cos\theta_{2}\\ \sin\theta_{2}\\ 1\end{pmatrix}$, respectively. Compute the set \begin{equation*} \arg\min_{\theta_{1},\theta_{2} \in [-\pi,\pi)}|f(\theta_{1},\theta_{2})|+|g(\theta_{1},\theta_{2})| \end{equation*}

Is there any intuition how to solve it?

I am trying to tackle the following problem:

Let $A_{f},A_{g} \in \mathbb{R}^{3 \times 3}$ be symmetric matrices and let $f: [-\pi,\pi)^{2} \to \mathbb{R}$ and $g: [-\pi,\pi)^{2} \to \mathbb{R}$ that map $(\theta_{1},\theta_{2})$ to $(\cos\theta_{1}, \sin\theta_{1}, 1)A_{f}\begin{pmatrix}\cos\theta_{2}\\ \sin\theta_{2}\\ 1\end{pmatrix}$ and $(\cos\theta_{1}, \sin\theta_{1}, 1)A_{g}\begin{pmatrix}\cos\theta_{2}\\ \sin\theta_{2}\\ 1\end{pmatrix}$, respectively. Compute the set \begin{equation*} \arg\min_{\theta_{1},\theta_{2} \in [-\pi,\pi)}|f(\theta_{1},\theta_{2})|+|g(\theta_{1},\theta_{2})| \end{equation*}

Is there any intuition how to solve it?