$\displaystyle p \equiv 2 (mod 3) $ and $\displaystyle p-1 = 4q$ with p and q distinct primes.

Show that:

$\displaystyle 3^{2q} \not\equiv 1 (mod p) $

I've tried various thing but I can't seem to find a contradiction (after assuming 3^(2q) == 1 mod p).

Can anyone point me in the right direction please??