If \( f(x)=\tan ^{-1}\left(\frac{\sqrt{1-4 x^{2}}-2 \sqrt{3} x}{\sqrt{3-12 x^{2}}+2 x}\right) \)...

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If \( f(x)=\tan ^{-1}\left(\frac{\sqrt{1-4 x^{2}}-2 \sqrt{3} x}{\sqrt{3-12 x^{2}}+2 x}\right) \) then the value of \( f\left(\frac{\sqrt{3}+1}{4 \sqrt{2}}\right)-f\left(\frac{1}{2 \sqrt{2}}\right) \) is equal to
(a) \( \frac{-5 \pi}{12} \)
(b) \( \frac{-\pi}{12} \)
(c) \( \frac{-\pi}{6} \)
(d) \( \frac{5 \pi}{12} \)
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