Thomas' Calculus 13th Edition

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