Find the number of solution of `theta in [0,2pi]` satisfying the equation `((log)_(sqrt(3))tantheta(sqrt((log)_(tantheta)3+(log)_(sqrt(3))3sqrt(3))=-1`

Explanation

`log_(sqrt3)tantheta[sqrt(log_tantheta 3+log_sqrt3 3sqrt3)]=-1`

`log_(sqrt3) tantheta[sqrt(2/log_sqrt3 tantheta)+3)]=-1`

`ysqrt(2/y+3)=-1`

`y^2(2/y+3)=1`

`2y+3y^2=1`

`3y^2+2y-1=0`

`3y(y+1)-1(y+1)=0`

`(y+1)(3y-1)=0`

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