A line in the 3-dimensional space makes an angle θ (0 < θ ≤ π/2) with both the x and y axes, then the set of all values of θ is the interval :

Sum of square of direction cosines is 1. Let's assume α is the angle with x, β with y and γ with z. α, β, γ ∈ [0, π/2]

Now, cos²α + cos²β + cos²γ = 1

But it is given that, α = β = θ

∴ cos²θ + cos²θ + cos²γ = 1

⇒ 2cos²θ = 1 - cos²γ

⇒ 2cos²θ = sin²γ

⇒ cosθ = sinγ / √2

As γ ∈ [0, π/2], then θ ∈ [π/4, π/2]