Telescoping trigonometric series: $\sin(x) \sec(3x) + \cdots+ \sin(3^{n}x) \sec(3^{n+1} x)$ How would you evaluate the sum of this series:
$$\sin(x) \sec(3x) + \sin(3x) \sec(3^{2}x) + \sin(3^{2}x) \sec(3^{3} x) + \cdots+ \sin(3^{n}x) \sec(3^{n+1} x)$$
I can tell it is a telescoping series but I am not able to get that one step that will cancel all terms

Lab Bhattacharjee has provided the necessary components to evaluate the series.
The series is seen as:
\begin{align}
\sum_{k=0}^{n} \frac{ \sin(3^{k} x) }{ \cos(3^{k+1} x)} &= \frac{1}{2} \sum_{k=0}^{n} \left( \tan(3^{k+1} x) - \tan(3^{k} x) \right) \\
&= \frac{1}{2} \left( \tan( 3^{n+1} x) - \tan(x) \right).
\end{align}
