Complex Complex Equations

Given $z=\cos(\frac{2\pi}{2n+1})+i\sin(\frac{2\pi}{2n+1})$ ,where n is a positive integer,find the equation whose roots are $\alpha=z+z^3+z^5+...+z^{2n-1}$ and $\beta=z^2+z^4+z^6+...+z^{2n}$ .

The equation will be of form: $x^2+x+\frac{1}{k}sec^2(\frac{\pi}{2n+1})$ What is k?