need help on trigo qn!?

Question

solve the following equations

sin x = sin x tan x ,0< or equal x < or equal 360 degrees

ans :0 , 45 ,180,225,360 degrees

i would like to know how to get the ans 0, 180 and 360?

because i do in this method and only managed to get 2 answers from the 5 answers

sin x/ sin x tan x =1
1/ tan x =1
tan x =1 (1st/3rd quadrant)
basic angle = tan inverse 1
= 45 degrees

x = 45 , 180+45
= 45 , 225 degrees

Answer 1

sin x - sin x tan x = 0
sin x (1 - tan x) = 0
sin x = 0 , tan x = 1
x = 0° , 180° , 360° , 45° , 225°

Answer 2

you read problem incorrectly