#### Answer

$360^{\circ}$

#### Work Step by Step

Given that there are $16$ steps and each step in the spiral staircase is with the central angle $\frac{\pi}{8}$.
So the total angle covered by the staircase $=16\times \frac{\pi}{8}=2\pi$ that is, $360^{\circ}$.
Therefore a person climbing the spiral staircase will rotate at an angle of $360^{\circ}$.