This system is not linear in that it says sin instead of 2 sin - cos

This system is not linear in that it says sin instead of
2 sin α - cos β + 3 tan γ = 3
4 sin α + 2 cos β - 2 tan γ= 10
6 sin α - 3 cos β + tan γ = 9
and yet we can apply Gauss's Method. Do so. Does the system have a solution?