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Let $$f(x) = \int \frac{dx}{(3+4x^2)\sqrt{4-3x^2}}$$, $$|x| < \frac{2}{\sqrt{3}}$$. If $$f(0) = 0$$ and $$f(1) = \frac{1}{\alpha\beta}\tan^{-1}\left(\frac{\alpha}{\beta}\right)$$, $$\alpha, \beta > 0$$, then $$\alpha^2 + \beta^2$$ is equal to _____.
Correct Answer: 28
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