Answer
$1.76 $ rad.
Work Step by Step
The angle between intersecting planes is the angle between their normal vectors.
${\bf n_{1}}=\langle 2,2,2 \rangle, \quad {\bf n_{2}}=\langle 2,-2,-1 \rangle$
$\displaystyle \theta=\cos^{-1}\left( \frac{{\bf n_{1}}\cdot{\bf n_{2}}}{|{\bf n_{1}}|\cdot|{\bf n_{2}}|} \right)=\cos^{-1}(\frac{4-4-2}{\sqrt{4+4+4}\cdot\sqrt{4+4+1}})$
$=\displaystyle \cos^{-1}(\frac{-2}{2\sqrt{3}\cdot 3})$
$=\displaystyle \cos^{-1}(\frac{-\sqrt{3}}{3\cdot 3})$
$\approx 1.76$
