try to assign a variable like u to tanx
then establish a relation between tanx and tan2x
and then write both equations in terms of u and equate both to each other
and then solve the resultant equation for u
your solution comes as mentioned below
1. draw a curve of x vs sin(x/2)
2. draw a second curve of "x vs x/4"
The solution for x is where both the curves intersect. these are two points
x=0
and
x=3.8
you can find the resultant chart in attached file.