Prove that `5costheta+3cos(theta+pi/3)+3` lies between `-4a n d10.`

Explanation

To prove that \(5 \cos \theta + 3 \cos \left( \theta + \frac{\pi}{3} \right) + 3\) lies between \(-4\) and \(10\), we will follow these steps:

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