Linear programming [duplicate]

I have a function f[x_]:= 3*(x - Pi/2)*(Sin[4*x])^2 + 2*Cos[3*x], and I need to use LinearProgramming command to find coefficients c1, c2, c3 and c4 of a function g[x_]:= c1*Sin[2x] + c2*Sin[4x] + c3*Cos[x] + c4*Cos[3x], so that the maximum absolute error is minimized -> min (max Abs[f[x] - g[x]]), range x is from 0 to Pi. Can someone please help me?