Solution (source code)

= Solution

Use the <angle between two planes> defined as the acute angle between their <normal vectors>. The normals $(1,1,1)$ and $(-1,1,1)$ have dot product one and lengths $\sqrt3$. Thus
$$
\boxed{\phi=\cos^{-1}\!\left(\frac13\right)=70.5288^\circ.}
$$
Choosing an oriented rather than an acute interplanar angle could give the supplementary $109.4712^\circ$; it describes the same unoriented pair of <lattice planes>.