If the sum of all the solutions of the equation `8 cosx.(cos(pi/6+x)cos(pi/6-x)-1/2)=1` in `[0,pi]` is `k pi` then k is equal to

If the sum of all the solutions of the equation 8cos x*(cos((pi)/(6)+x)cos((pi)/(6)-x)-(1)/(2))=1 in [0,pi] is k pi then k is equal to

The sum ofall the solutions ofthe equation cos((pi)/(3)+x)*cos((pi)/(3)-x)=(1)/(4)x in[0,6 pi]

The sum of all the solution of the equation costhetacos(pi/3+theta)cos(pi/3-theta)=1/4theta in [0,6pi]

The sum of all the solutions in [0, 4pi] of the equation tan x+ cot x+1= cos (x+pi/4) is

The sum of the solutions in (0, 2pi) of the equation cos x cos ((pi)/(3)-x)cos((pi)/(3)+x)=(1)/(4) is

The number of solutions of the equation cos^(2)(pi)/3 cos x-(8pi)/3=1 in the interval [0,10pi] is