Trigonometry is so much fun!

Algebra Level pending

If tan ( α + β ) = 3 tan α \tan { \left( \alpha +\beta \right) = } 3\tan { \alpha } then what is the value of sin ( 2 α + β ) sin β \frac { \sin { \left( 2\alpha +\beta \right) } }{ \sin { \beta } } ?

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The picture has no relevant connection to the problem. It's just there because I found it funny.


The answer is 2.

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