The wavefronts of a light wave travelling in vacuum are defined by...

The equation of the wavefront is given by $x + y + z = c$.

The direction of propagation of a light wave is always perpendicular to its wavefront.

The normal vector to the plane $x + y + z = c$ represents the direction of propagation, which is $\vec{n} = \hat{i} + \hat{j} + \hat{k}$.

The angle $\alpha$ made by the direction of propagation with the X-axis (direction vector $\hat{i}$) is given by

$\cos \alpha = \dfrac{\vec{n} \cdot \hat{i}}{|\vec{n}| |\hat{i}|}$

$\cos \alpha = \dfrac{(\hat{i} + \hat{j} + \hat{k}) \cdot \hat{i}}{\sqrt{1^2 + 1^2 + 1^2} \sqrt{1^2}}$

$\cos \alpha = \dfrac{1}{\sqrt{3}}$

$\alpha = \cos^{-1} \left(\dfrac{1}{\sqrt{3}}\right)