question_answer

If\[\frac{\tan x}{2}=\frac{\operatorname{tany}}{3}=\frac{\operatorname{tanz}}{5}\]and \[x+y+z=\pi ,\]\[{{\tan }^{2}}x+{{\tan }^{2}}y+{{\tan }^{2}}z=\frac{38}{K}\], then K = ______.

Answer:

3