Answer
$\approx 1.83$ rad
Work Step by Step
The angle between two planes can be determined as:
$ \theta = \cos ^{-1} (\dfrac{a \cdot b}{|a||b|})$
Now, $a=\lt 1, \sqrt 2,-\sqrt 2 \gt$ and $b=\lt -1,1,1 \gt$
Here, $|a|=\sqrt{(1)^2+(\sqrt 2)^2+(-\sqrt 2)^2+(0)^2}= \sqrt {5}$ and $|b|=\sqrt{(-1)^2+(1)^2+(1)^2}=\sqrt {3}$
So, $ \theta =\cos ^{-1} (\dfrac{-1}{ ( \sqrt {5})(\sqrt 3)}) \approx 1.83$ rad