A line makes angle $\theta$ with $x\:\:and\:\:z\:\:axis.$ If it makes angle $\beta$ with $y\; axis$, where $sin^2 \beta=3sin^2\theta$, then $cos^2\theta=?$

Question

$(A)\:\:\large\frac{2}{3}\:\:\:\:\qquad\:\:(B)\:\:\frac{1}{5}\:\:\:\:\qquad\:\:(C)\:\:\frac{3}{5}\:\:\:\:\qquad\:\:(D)\:\:\frac{2}{5}.$