Find \(y\)?

Calculus Level 3

\[\lim_{x\to0 } \left [\left \lfloor \dfrac {\sin x}x \right \rfloor + \left \lfloor \dfrac x{\sin x} \right \rfloor + \left \lfloor \dfrac {\tan x}x \right \rfloor + \left \lfloor \dfrac x {\tan x} \right \rfloor + \lfloor \cos x \rfloor \right] = y + \dfrac1y\]

Find the value of \(y\) satisfying the equation above.

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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