Variations of a sinc function

Question

Consider the following function

\begin{align} G(\omega_t) = \frac{1}{N_t}\text{exp} \bigg( j \pi \Delta_t \omega_t (N_t-1)\bigg) \frac{\sin (\pi N_t \Delta_t \omega_t)}{\sin (\pi\Delta_t \omega_t)} \end{align}

with the following assumptions: $N_t$ is positive integer, $\Delta_t$ is a positive number between $]0:1[$, and $\omega_t \in[-2:2]$.

Example 1: of a plot of this function $(\Delta_t=0.5, N_t=256)$ is shown below.

Example 2: $N_t=1, \Delta_t=0.5$ the plot would be

Question: Can anyone think of a case when $N_t >1$ and where the function $$ G(\omega_t)=1 \,\,\,\,\,\,\, \forall \ \omega_t$$

Answer 1

When $\Delta_t=0$, and $N_t > 1$, $G=1$ as well.