\(\displaystyle 16\pi= 8(2\pi)\) so the interval is 8 times around a circle. The line y= -1 crosses the circle \(\displaystyle x^2+ y^2= 1\) twice so this will be true 16 times. You can use a calculator, or simple symmetry considerations, to determine one of those, then use the fact that tangent is periodic with period [itex]\pi[/itex].
