Since it is given that $\overrightarrow a,\overrightarrow b$ lie on the plane $P_1$,
Normal to $P_1$ is $\perp$ to both $\overrightarrow a\:\:and\:\:\overrightarrow b$.
$\Rightarrow\:\overrightarrow n_1=\overrightarrow a\times\overrightarrow b$
Similarly normal to $P_2$= $\overrightarrow n_2$ is $\perp$ to $\overrightarrow c\:\:and \:\:\overrightarrow d$
$\Rightarrow\:\overrightarrow n_2=\overrightarrow c\times\overrightarrow d$
Given that $(\overrightarrow a\times\overrightarrow b)\times (\overrightarrow c\times\overrightarrow d)=0$
$\Rightarrow\:\overrightarrow n_1\times\overrightarrow n_2=0$
$\Rightarrow$ Both the planes are parallel.
$\therefore$ The angle is $0$.