If $f:R\to [-\frac{\pi}{4}, \frac{\pi}{2})$, $f(x)=\tan^{-1} (x^4-x^2 -\frac 74 +\tan^{-1} \alpha)$, find $\alpha$

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I simplified the expression to $$\tan (f(x)) = (x^2 -\frac 12)^2 + (\tan^{-1} \alpha -2)$$

How do I solve further???