Figure-It-Out Function! - Part 6: The Second Reciprocal

Algebra Level 5

Let there be a function $$f(x)$$, such that

$$f(x)=\frac{1}{f(x-1)+f(x+1)}$$

$$f(1)=2$$, $$f(2)=1$$

Find $$(f(2014)f(2015))^{(f(2012)f(2013))^{...^{...^{(f(2)f(3))^{f(1)}}}}}$$

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