Linear combination of orthogonal-matrix entries

For some $a\le 0$ and $b\in\mathbb{R}$, let $$A=\begin{pmatrix}0&a&b\ -\frac1{\sqrt{2}}&\frac1{\sqrt{6}}&\frac1{\sqrt{3}}\ \frac1{\sqrt{2}}&\frac1{\sqrt{6}}&\frac1{\sqrt{3}}\end{pmatrix}.$$ If $A$ is an orthogonal matrix, then the value of $a\sqrt{6}+4b\sqrt{3}$ is equal to __________ (answer in integer)