If T is the period of the function fx=8x+7+tan2πx+cot2πx-8x  (where [.] denotes the greatest integer function), then the value of T  is ______

fx=8x+7+tan2πx+cot2πx-8x             =8x-8x+7+tan2πx+cot2πx             =-8x+tan2πx+cot2πx+7Period  of  8x  is  1/8.Also,   tan2πx+cot2πx=sin2πxcos2πx+cos2πxsin2πx                                                      =1sin2πxcos2πx=2  cosec  4πxNow, period of 2    cosec  4πx    is   1/2.   Then   period   of   2  cosec  4πx  is  1/4Therefore, period is L.C.M of  18   and   14   which   is  14.