If $p\equiv 2 \pmod{3}$ evaluate :

Question

$S=$ #$\{x\in \mathbb{F}_p^{*} \ / \ x^{\frac{p-2}{3}}=1 \}$ ?

Let consider $\phi : \mathbb{F}_p^* \to \mathbb{F}_p^*, \ x \mapsto x^{\frac{p-2}{3}}$ a homomorphism. By property we will have : #$\ker(\phi)$$=$#$S$.

But how to determine #$\ker(\phi)$ ?

Thanks in advance !