Matrices And Determinants

For $\alpha, \beta \in[0,2 \pi]$ and $\gamma \in[0, \pi)$ consider the system of equations

$$ \begin{aligned} & 2 \sin \alpha-\cos \beta+3 \tan \gamma=3 \\ & 4 \sin \alpha+2 \cos \beta-2 \tan \gamma=2 \\ & 6 \sin \alpha-3 \cos \beta+\tan \gamma=9 \end{aligned} $$

Then, which one of the following is true?