Multiple choice

If $1$ lies between the roots of the quadratic equation $3 x ^ { 2 } - ( 3 \sin \theta ) x - 2 \cos ^ { 2 } \theta = 0 ,$ then $:$

  1. $- \dfrac { \pi } { 3 } < \theta < \dfrac { 5 \pi } { 3 }$
  2. $n \pi < \theta < 2 n \pi$
  3. $2 n \pi + \dfrac { \pi } { 6 } < \theta < 2 n \pi + \dfrac { 5 \pi } { 6 }$

  4. none of these
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