A line makes an angle $\alpha$, $\beta$, $\gamma$ with the $x$, $y$, and $z$ axes respectively. Then the value of ${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma$ is:

Let $l,m,n$ be the direction cosines of the line, where $l=\cos \alpha$, $m=\cos \beta$, and $n=\cos \gamma$.We know that the sum of the squares of the direction cosines of a line is equal to unity:
$${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$$
Using the identity ${\cos }^2\theta =1-{\sin }^2\theta$:
$$(1-{\sin }^2\alpha )+(1-{\sin }^2\beta )+(1-{\sin }^2\gamma )=1$$
$$3-({\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma )=1$$
$$3-1={\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma$$
$${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma =2$$