For all values of $\theta$, the values of $3- \cos \theta+ \cos \bigg(\theta+\large\frac{\pi}{3}\bigg)$ lie in the interval :

Question

\[\begin {array} {1 1} (a)\;[-2,3] & \quad (b)\;[-2,1] \\ (c)\;[2,4]& \quad (d)\;[1,5] \end {array}\]