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If $$f(t) = \int_0^{\pi} \frac{2x \, dx}{1 - \cos^2 t \sin^2 x}$$, $$0 < t < \pi$$, then the value of $$\int_0^{\frac{\pi}{2}} \frac{\pi^2 dt}{f(t)}$$ equals _________
Correct Answer: 1
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