Question 858136
I'm going to use x in place of theta



sin(x)+tan(-x)=0



sin(x)-tan(x)=0 ... since tan(x) is odd



sin(x)-sin(x)/cos(x)=0



sin(x)*cos(x)/cos(x)-sin(x)/cos(x)=0



( sin(x)*cos(x)-sin(x) )/cos(x)=0



sin(x)*cos(x)-sin(x) = 0*cos(x)



sin(x)*cos(x)-sin(x) = 0



sin(x)( cos(x)-1 ) = 0



sin(x) = 0 or cos(x)-1 = 0



sin(x) = 0 or cos(x) = 1



x = arcsin(0) or x = arccos(1)



x = 0, pi or x = 0



So if x is in the interval [0, 2pi), then the solutions are: x = 0, x = pi