The sum of squares of direction cosines of a vector is 1.
Let the angles made by vector be α, β, θ. Then, we get
cos2α + cos2β + cos2θ = 1
Given that \(\alpha=\cfrac{\pi}3\) and \(\beta=\cfrac{\pi}2,\) we have to calculate θ
Hence, \(\theta=\cfrac{\pi}6\)