Dominating Twos

Algebra Level 4

\[ \large {\sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt 2}}}} \div {\sqrt{2 - \sqrt{2 - \sqrt{2 - \sqrt 2}}}} \]

If \(X\) equals to the expression above, determine the value of \( \left \lceil 10^4 X \right \rceil \).

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