To answer this question, we have that we need to find the values for t where the tangent function will be equal to zero.
We have that:
![\tan t=0](https://img.qammunity.org/2023/formulas/mathematics/college/c3ty65bg9j10le4jarpdqnip5ji49njuxs.png)
And, if we see that the function tangent is equal to:
![\tan t=(\sin t)/(\cos t)](https://img.qammunity.org/2023/formulas/mathematics/college/iwxu3pfluowsj39nckmbzpfcxvf56qher3.png)
We need to find, in the interval:
![0\leq t\leq2\pi](https://img.qammunity.org/2023/formulas/mathematics/college/etaqj5brjsw5x24s4e5k2ecgjz3ajxjoi4.png)
The values for which sin(t) = 0. If we see the unit circle, the points, in this interval, where sin(t) = 0 are t = 0, t = pi, and t = 2*pi.
Therefore, we have that the points for tan(t) = 0 are, therefore (in the given interval):
![\tan t=0,t=0,t=\pi,t=2\pi](https://img.qammunity.org/2023/formulas/mathematics/college/xqqbg08kxzl0g055tem18d5esggiggqkha.png)