Euler sine product and the continued fraction of π

The Euler sine product and the continued fraction of $\pi$ are discussed in this article. Some of the infinite series for cotangent and its derivative are obtained by implementing the concept of Euler sine product and some of the standard series are derived as the immediate consequence of the main results. Furthermore, the continued fraction for odd powers of $\pi$ similar to the expression of $\pi$ derived by Brouncker is presented in this article. Meanwhile, an expression relating the Basel's constant and the cotangent function is obtained as follows: \begin{equation*} \frac{\coth{r}}{2}-\frac{1}{2r}=\sum_{n\in\mathbb{N}}\frac{2^{2n}}{2(2n)!}B_{2n}r^{2n-1}. \end{equation*}