If $a$ and $b$ are nonzero real numbers such that $|a| \neq |b|$, compute the value of the expression
\[
  \left( \frac{b^2}{a^2} + \frac{a^2}{b^2} - 2 \right) \times
  \left( \frac{a + b}{b - a} + \frac{b - a}{a + b} \right) \times
  \left( 
    \frac{\frac{1}{a^2} + \frac{1}{b^2}}{\frac{1}{b^2} - \frac{1}{a^2}}
      - \frac{\frac{1}{b^2} - \frac{1}{a^2}}{\frac{1}{a^2} + \frac{1}{b^2}}
  \right).
\]

Let's think step by step and output the final answer within \boxed{}.
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