A line makes angle θ with x-axes as well as z-axis. If the angle β, which it makes with y-axis is such that $sin^2β=3sin^2θ$, then $cos^2θ$ is:

$\frac{3}{5}$

If a line makes the angle α,β,γ with x,y,z axix respectively then

$l^2+m^2+n^2=1$

$⇒2l^2+m^2=1$ or $2n^2+m^2=1$

$⇒2cos^2θ=1−cos^2β(α=γ=θ)$

$2cos^2θ=sin^2β$

$⇒2cos^2θ=3sin^2θ$

$⇒5cos^2θ=3⇒cos^2θ=\frac{3}{5}$