A line makes an angle of $\frac{\pi}{4}$ with each of the $x$- and $y$-axes. What angle does it make with the $z$-axis?

Explanation

1. 01

   $\cos^{2}\gamma = 1 - \cos^{2}\frac{\pi}{4} - \cos^{2}\frac{\pi}{4} = 1 - \frac{1}{2} - \frac{1}{2} = 0$.

2. 02

   $\cos \gamma = 0$, so $\gamma = \frac{\pi}{2}$.