Find the best approximation to $z$ by vectors of the form $c_1{v}_1+c_2{v}_2.$

$z=\left[\begin{array}{c}3\\ -6\\ 2\\ 3\end{array}\right],v_1=\left[\begin{array}{c}3\\ 1\\ 2\\ -1\end{array}\right],v_2=\left[\begin{array}{c}1\\ -1\\ 0\\ 2\end{array}\right]$

The best approximation to $z$ is $.($Simplify your answer.$)$