A line makes the same angle α with each of the x and y axes. If the angleθ, which it makes with the z-axis, is such thatsin2θ=2sin2α, then what is the value ofα?

[a] Since l2+m2+n2=1 ∴cos2α+cos2α+cos2θ=1          ????(i) (∵ A line makes the same angle αwith x and y-axes and θ with z-axis) Also, sin2θ=2sin2α ⇒1=cos2θ=2(1−cos2α)(∴sin2A+cos2A=1) ⇒cos2θ=2cos2α−1                 ????(ii) ∴ From equation (i) and (ii) 2cos2α+2cos2α−1=1 ⇒4cos2α=2⇒cosα=±12√⇒α=π4,3π4