Suppose that a, b, and c are real numbers greater than 1. Then the value of $$\frac{1}{1+\log a^{2} c\frac{c}{a}} + \frac{1}{1+\log b^{2} c\frac{a}{b}} + \frac{1}{1+\log c^{2} a\frac{b}{c}}$$ is .............
Correct Answer: 3
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