JEE Math Practice Question

If [x] denotes the greatest integer $$ \le $$ x, then the system of linear equations [sin $$\theta $$]x + [–cos$$\theta $$]y = 0, [cot$$\theta $$]x + y = 0

1. A.has a unique solution if $$\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right)$$ and have infinitely many solutions if $$\theta \in \left( {\pi ,{{7\pi } \over 6}} \right)$$
2. B.have infinitely many solutions if $$\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right)$$ and has a unique solution if $$\theta \in \left( {\pi ,{{7\pi } \over 6}} \right)$$
3. C.have infinitely many solutions if $$\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right) \cup \left( {\pi ,{{7\pi } \over 6}} \right)$$
4. D.has a unique solution if $$\theta \in \left( {{\pi \over 2},{{2\pi } \over 3}} \right) \cup \left( {\pi ,{{7\pi } \over 6}} \right)$$