Past exam of the condensed matter physics course of the University of Oxford / 2017 / 1 / c / i / 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 $\sqrt{3}$. ThusChoosing an oriented rather than an acute interplanar angle could give the supplementary $109.4712^{\circ }$; it describes the same unoriented pair of lattice planes.