麻烦各位大神了，帮忙解一下这道数学题吧，拜托了谢谢！！！

f(x) = sinxcos(π/6) - cosxsin(π/6) +cosxcos(π/3) + sinxsin(π/3) + cosx + a= √3sinx + cosx + a = 2[ (√3/2)sinx + (1/2)cosx ] + a=2[ cos(π/6)sinx +sin(π/6)cosx ] + a= 2sin( x + π/6 ) + a；T = 2π1、 2 +a = 1，a = -1；2、x +π/6 = -π/2，x =-2π/3；单调增区间 ( -2π/3+2kπ，π/3+2kπ )；3、2sin( x +π/6 ) - 1 < 0，sin( x +π/6 ) < 1/2，π/6 < x +π/6 < 5π/6，0<x < 2π/3；x的取值范围是 (2kπ，2kπ +2π/3 )，k∈Z 。