<prompt> Pata thamani ya chini ya2 cos theta frac1sin theta sqrt2 tan thetakwa 0 theta fracpi2.  <response>: Na AM-GM,2 cos theta frac1sin theta sqrt2 tan theta ge 3 sqrt32 cos theta cdot frac1 sin theta cdot sqrt2 tan theta 3 sqrt2.Usawa hutokea wakati theta fracpi4, hivyo thamani ya chini zaidi ni 3 sqrt2. 