Floor strikes

Geometry Level 3

\[\lfloor y+\lfloor y \rfloor \rfloor =2 \cos x\]

Find the number of solutions of the above equation if \[y=\frac{1}{3}\lfloor \sin x+\lfloor \sin x +\lfloor \sin x \rfloor \rfloor \rfloor \]

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

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