Start by multiplying through by \(\cos \theta\) to eliminate the fraction:

\(2 \cos^2 \theta = 7 \cos \theta - 3\)

Rearrange to form a quadratic equation:

\(2 \cos^2 \theta - 7 \cos \theta + 3 = 0\)

Factor the quadratic equation:

\((2 \cos \theta - 1)(\cos \theta - 3) = 0\)

Set each factor to zero and solve for \(\cos \theta\):

\(2 \cos \theta - 1 = 0\) gives \(\cos \theta = \frac{1}{2}\)

\(\cos \theta - 3 = 0\) gives \(\cos \theta = 3\) (not possible since \(|\cos \theta| \leq 1\))

For \(\cos \theta = \frac{1}{2}\), \(\theta = \pm 60^\circ\) within the given range.

Thus, \(\theta = -60^\circ\) and \(\theta = 60^\circ\).