You want to solve

    2sin(x) + 2tan(x) = 0.


The domain of this equation are all real numbers except of  x = ,  where cos(x) = 0.


Rewrite in the form

    2sin(x) +  = 0.


In the domain, multiply both sides by  .


Since  cos(x) =/= 0,  you will get an equivalent equation

    sin(x)*cos(x) + sin(x) = 0.


Factor

    sin(x)*(cos(x) + 1) = 0.


So, either sin(x) = 0,  giving the solutions  x = ,  k = 0, +/-1, +/-2, . . .          (1)

    or  cos(x) + 1 = 0,  cos(x) = -1,  giving  x = ,  k = 0, +/-1, +/-2, . . .    (2)



The set (2) is part of set (1) - so, the general solution to the given equation is the set

    x = ,  k = 0, +/-1, +/-2, . . .


ANSWER.  The general solution to the given equation is the set  x = ,  k = 0, +/-1, +/-2, . . .