I am looking for a closed-form formula for the following sum: $\sum_{k=0}^{N}{\frac{sin^{2}(\frac{k\pi}{N})}{a \cdot sin^{2}(\frac{k\pi}{N})+1}}=\sum_{k=0}^{N}{\frac{1}{a+cosecant^{2}{\frac{k\pi}{N}}}}$. Is such a formula known?

I am looking for a closed-form formula for the following sum:

$\displaystyle \sum_{k=0}^{N}{\frac{\sin^{2}(\frac{k\pi}{N})}{a \cdot \sin^{2}(\frac{k\pi}{N})+1}}=\sum_{k=0}^{N}{\frac{1}{a+\csc^{2}(\frac{k\pi}{N})}}$. 

Is such a formula known?

I am looking for a closed-form formula for the following sum: $\sum_{k=0}^{N}{\frac{sin^{2}(\frac{k\pi}{N})}{a \cdot sin^{2}(\frac{k\pi}{N})+1}}=\sum_{k=0}^{N}{\frac{1}{a+secant^{2}{\frac{k\pi}{x}}}}$. Is such a formula known?

I am looking for a closed-form formula for the following sum: $\sum_{k=0}^{N}{\frac{sin^{2}(\frac{k\pi}{N})}{a \cdot sin^{2}(\frac{k\pi}{N})+1}}=\sum_{k=0}^{N}{\frac{1}{a+cosecant^{2}{\frac{k\pi}{N}}}}$. Is such a formula known?