Let α and β be the roots of the quadratic equation x^2 sin θ-x( sin θ cos θ+1)+ cos θ=0 (0<θ<45^°), and α<β. Then Σ_n=0^∞(α^n+((-1)^n)/(β^n)) is…

Let $\displaystyle \alpha$ and $\displaystyle \beta$ be the roots of the quadratic equation $$x^2 \sin \theta-x(\sin \theta \cos \theta+1)+\cos \theta=0 $$ $\displaystyle \left(0<\theta<45^{\circ}\right)$, and $\displaystyle \alpha<\beta$. Then $\displaystyle \sum_{n=0}^{\infty}\left(\alpha^n+\frac{(-1)^n}{\beta^n}\right)$ is equal to :