A line makes an angleθ with each of the x- and z-axes. If the angle  β which it makes with the y-axis, is such that sin2⁡β=3sin2⁡θ, then cos2⁡θ

Here   sin2⁡β=3sin2⁡θ,-----(i)By the question, cos2⁡θ+cos2⁡θ+cos2⁡β=1-------(ii)⇒ cos2⁡β=1−2cos2⁡θ-------(iii)Adding (i) and (iii), we get 1=1+3sin2⁡θ−2cos2⁡θ=1+31−cos2⁡θ−2cos2⁡θor  5cos2⁡θ=3or  cos2⁡θ=35