If [x] denotes the greatest integer ≤ x, then the system of linear equations [sin θ ]x + [–cos θ ]y = 0, [cot θ ]x + y = 0

has a unique solution if θ ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π 3 2 , 2 and have infinitely many solutions if θ ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π 6 7 ,
have infinitely many solutions if θ ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π 3 2 , 2 and has a unique solution if θ ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π 6 7 ,
have infinitely many solutions if θ ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π 3 2 , 2 ∪ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π 6 7 ,
has a unique solution if θ ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π 3 2 , 2 ∪ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π 6 7 ,

Correct answer: have infinitely many solutions if θ ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π 3 2 , 2 and has a unique solution if θ ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π 6 7 ,

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