Evaluate the following expression :

\[\underset { x\rightarrow 0 }{ lim } \frac { \left( \sqrt { \left( 1-cos\quad x \right) +\sqrt { \left( 1-cos\quad x \right) +\sqrt { \left( 1-cos\quad x \right) +.........\infty } } } \right) -1 }{ { x }^{ 2 } } \]

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