Let α=3+4+8+9+13+14+… upto 40 terms. If ( tan β)^((α)/1020) is a root of the equation x^2+x-2=0, β ∈(0, (π)/2), then sin^2 β+3 cos^2 β is equal to:

Let $\displaystyle \alpha=3+4+8+9+13+14+\ldots$ upto $\displaystyle 40$ terms. If $\displaystyle (\tan \beta)^{\frac{\alpha}{1020}}$ is a root of the equation $\displaystyle x^2+x-2=0, \beta \in\left(0, \frac{\pi}{2}\right)$, then $\displaystyle \sin ^2 \beta+3 \cos ^2 \beta$ is equal to :