value of $x$ in Trigonometric equation Find real $x(0<x<180^\circ)$ in 
$\tan(x+100^\circ)=\tan(x-50^\circ)+\tan(x)+\tan(x+50^\circ)$ 
what i try
$\displaystyle \tan(x+100^\circ)-\tan(x)=\tan(x+50^\circ)+\tan(x-50^\circ)$
$\displaystyle \frac{\sin(100^\circ)}{\cos(x+100^\circ)\cos x}=\frac{\sin(2x)}{\cos(x+50^\circ)\cos(x-50^\circ)}$
$\displaystyle \frac{\sin(100^\circ)}{\cos(2x+100^\circ)+\cos(100^\circ)}=\frac{\sin(2x)}{\cos(2x)+\cos(100^\circ)}$
How do i solve further
Help me please 

Let $\cos100^\circ=a$ and $\sin100^\circ=b$; let $\cos2x=X$ and $\sin2x=Y$. The final equation can be written
$$
\frac{b}{aX-bY+a}=\frac{Y}{X+a}
$$
that is,
$$
bX+ab=aXY-bY^2+aY
$$
together with $X^2+Y^2=1$. This is the intersection between a hyperbola and a circle, so generally a degree 4 equation.

