tantheta tan(60-theta) tan(60+theta)=tan3theta

Let @ be theta

sin@ sin(60-@) sin (60+@) = 1/4 sin3@

and cos@ cos(60-@) cos (60+@) = 1/4 cos3@

hence tan@ is equal to

sin@ sin(60-@) sin (60+@) = 1/4 sin3@  / cos@ cos(60-@) cos (60+@) = 1/4 cos3@

that is equal to tan3@