If the range of f(θ)=(sin^4 θ+3 cos^2 θ)/(sin^4 θ+ cos^2 θ), θ ∈ R is [α, β], then the sum of the infinite G.P., whose first term is 64 and the…

If the range of $\displaystyle f(\theta)=\frac{\sin ^4 \theta+3 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta}, \theta \in \mathbb{R}$ is $\displaystyle [\alpha, \beta]$, then the sum of the infinite G.P., whose first term is $\displaystyle 64$ and the common ratio is $\displaystyle \frac{\alpha}{\beta}$, is equal to $\displaystyle \_\_\_\_$.