find the closed form of $\sum_{k=1}^\infty\left(\frac{\sec{kz}}{k^2}\right)^2$

Question

How to evaluate $\displaystyle\sum_{k=1}^\infty\left(\frac{\sec{(k\pi\sqrt{5})}}{k^2}\right)^2$?

In general, how to find the closed form of infinite series $\displaystyle\sum_{k=1}^\infty\left(\frac{\sec{(kz)}}{k^2}\right)^2$ in term of variable $z$ ? Thanks in advance.