If `a leq 3 cos (theta+pi/3)+5cos theta+3 leq b`, find `a and b`, where a is the minimum value & b is the If a maximum value.

Explanation

To solve the problem, we need to find the minimum value \( a \) and the maximum value \( b \) of the expression \( 3 \cos(\theta + \frac{\pi}{3}) + 5 \cos \theta + 3 \).

### Step 1: Rewrite the expression
We start with the expression:
\[ 3 \cos(\theta + \frac{\pi}{3}) + 5 \cos \theta + 3 \]
Using the cosine addition formula, \( \cos(A + B) = \cos A \cos B - \sin A \sin B \), we can rewrite \( \cos(\theta + \frac{\pi}{3}) \):
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