Indefinite Integrals

Let $f(x)=\int \frac{d x}{\left(3+4 x^{2}\right) \sqrt{4-3 x^{2}}},|x|<\frac{2}{\sqrt{3}}$. If $f(0)=0$

and $f(1)=\frac{1}{\alpha \beta} \tan ^{-1}\left(\frac{\alpha}{\beta}\right)$,

$\alpha, \beta>0$, then $\alpha^{2}+\beta^{2}$ is equal to ____________.