Find the value of parameter $m$ such that the equation has real solutions...

Question

For which values of real parameter "m" the equation:$$\sqrt3*|\tan x+\cot x|=4m$$ has real solutions? My only thought is that $m\gt 0$ because the right part of the equation is an absolute value which is always positive. That's the only thing I can say. I hope you'll add some more ideas, and help me solve this exercise. Thank you!

Answer 1

Hint: $$\tan x+\cot x=\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x} =\frac{\sin^2x+\cos^2x}{\cos x\sin x}=\frac{2}{\sin2x}\ .$$