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If ; 1 sin 1 sin 1 sin 1 sin 1 A ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ θ − − θ θ − θ = then for all ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π ∈ θ 4 5 , 4 3 , det (A) lies in the interval :

1. ⎥ ⎦ ⎤ ⎜ ⎝ ⎛ 3 , 2 3
2. ⎥ ⎦ ⎤ ⎜ ⎝ ⎛ 2 3 , 0
3. ⎟ ⎠ ⎞ ⎢ ⎣ ⎡ 4 , 2 5
4. ⎥ ⎦ ⎤ ⎜ ⎝ ⎛ 2 5 , 1

Correct answer: ⎥ ⎦ ⎤ ⎜ ⎝ ⎛ 3 , 2 3

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