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

A

2

B

$$\frac{7}{4}$$

C

$$\frac{5}{2}$$

D

$$\frac{3}{2}$$