The question is The minimum value of x for which $\tan(x+100)=\tan(x+50)\tan(x)\tan(x-50)$
Here is what I've tried so far:
In the R.H.S- $$\frac {\sin(x+50)\sin(x-50)\sin(x)}{\cos(x+50)\cos(x-50)\cos(x)}\implies \frac {(\sin^2x-\sin^250)\sin x}{(\cos^2x-\sin^250)\cos x}$$
But, I think I am proceeding wrong because my process is not yielding any result. Kindly help me out.