A light wave is propagating with plane wave fronts of the type...

The direction of propagation of light is perpendicular to the wave front and is symmetric about $\mathrm{x}, \mathrm{y}$ and z axis.
$\therefore$ Angle made by the light with $\mathrm{x}, \mathrm{y} \& \mathrm{z}$ axis is same.
$\therefore \quad \cos \alpha=\cos \beta=\cos \gamma(\alpha, \beta \& \gamma$ are angle made by light with $\mathrm{x}, \mathrm{y} \& \mathrm{z}$ axis respectively)
Also $\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1$ [Sum of direction cosines]
$\therefore \alpha=\cos ^{-1} \frac{1}{\sqrt{3}}$