$If \ f( \theta ) \ = \frac {1}{3} \ {4 (\cos^6 \theta + \sin^6 \theta)} \ then, \\ \lim _{ n\rightarrow \infty }{ \frac { 1 }{ n } } \left\lfloor \sqrt { f\quad (\frac { 1 }{ n } ) } \right\rfloor +\left\lfloor \sqrt { f\quad (\frac { 2 }{ n } ) } \right\rfloor +\left\lfloor \sqrt { f\quad (\frac { 3 }{ n } ) } \right\rfloor +......+\left\lfloor \sqrt { f\quad (\frac { n }{ n } ) } \right\rfloor$ Sorry it took me LONG time ! sorry @nitz