A line which makes angle 60° with y-axis and z-axis, then the angle which it makes with x-axis is:

Given that $\beta =\gamma ={60}^{\circ }$ i.e.

$m=\cos \beta =\cos {60}^{\circ }=1/2,n=\cos \gamma =\cos {60}^{\circ }=1/2$

$\begin{array}{l}\because \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{l}^2+m^2+n^2=1\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{l}^2=1-\frac{1}{4}-\frac{1}{4}=\frac{1}{2}\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}l=\frac{1}{\sqrt{2}}\Rightarrow \cos \alpha =\frac{1}{\sqrt{2}}\Rightarrow \alpha ={45}^{\circ }\end{array}$