Evaluate

\[\lim _{ n\rightarrow \infty }\underbrace { { \left( \sin { \left( \cos { \left( \tan { \left( \sin { \left( \cos { \left( \tan { \left( ... \right) } \right) } \right) } \right) } \right) } \right) } \right) } }_{n}\]

rounded to three decimal places.

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