\[ \large \displaystyle f(n, \theta) = \prod_{r=1}^n \left [1 - \tan^2 \left ( \frac \theta {2^r} \right ) \right] \]

Suppose we have a function of \( f(n,\theta) \) as above, find the value of \( \displaystyle \lim_{\theta\to 0}\lim_{n\to \infty} f(n, \theta) \).

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