follow by definition

Wait—what if the equation is:

\cos(\theta + 60^\circ) + \cos(\theta - 60^\circ) = \sqrt{3} \cdot \cos\theta

But that's identity. So instead, suppose the intended equation is:

\cos(\theta + 60^\circ) + \cos(\theta - 60^\circ) = \sqrt{3}

\Rightarrow \cos\theta = \sqrt{3} \quad \text{(impossible)}

Thus, no solution. But to fix, suppose the equation is:

2\cos\theta = \sqrt{3} \Rightarrow \cos\theta = \frac{\sqrt{3}}{2}

\Rightarrow \theta = 30^\circ \text{ or } 330^\circ

Smallest positive is $30^\circ$. But not matching. Re-express the identity correctly:

\cos(\theta + 60^\circ) + \cos(\theta - 60^\circ) = 2\cos\theta\cos 60^\circ = 2\cos\theta \cdot \frac{1}{2} = \cos\theta

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