Multiple choice

If $ \alpha $ and $ \beta $ are roots of equation $ \frac { 3 } { 4 } \sin \left( \frac { \theta } { 9 } \right) = \sin ^ { 3 } \theta + 3 \sin ^ { 3 } \left( \frac { \theta } { 3 } \right) + 9 \sin ^ { 3 } \left( \frac { \theta } { 9 } \right) + \frac { 1 } { 4 \sqrt { 2 } } $ for $ 0 < \theta < \frac { \pi } { 2 } $ then $ \tan \alpha + \tan \beta $ is equal to

  1. $

    2 + \sqrt { 3 }

    $
  2. $

    3 + \sqrt { 3 }

    $
  3. $

    3 - \sqrt { 3 }

    $
  4. $

    2 - \sqrt { 3 }

    $
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C Correct answer

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