$a)f\left(x\right)=\sqrt{3}x+2\Rightarrow a=\sqrt{3}\Rightarrow \mathrm{tg}\alpha =\sqrt{3}\Rightarrow \alpha ={60}^o$

$b)f\left(x\right)=x-\frac{\sqrt{3}}{3}\Rightarrow a=1\Rightarrow \mathrm{tg}\alpha =1\Rightarrow \alpha ={45}^o$