Start with the equation \(3 \sin^2 \theta - 2 \cos \theta - 3 = 0\).

Use the identity \(\sin^2 \theta = 1 - \cos^2 \theta\) to rewrite the equation:

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

Simplify to get:

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

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

Factor the equation:

\(\cos \theta (3 \cos \theta + 2) = 0\)

Set each factor to zero:

1. \(\cos \theta = 0\)

\(\theta = 90^\circ\)

2. \(3 \cos \theta + 2 = 0\)

\(\cos \theta = -\frac{2}{3}\)

\(\theta = 131.8^\circ\) (to 1 decimal place)

Thus, the solutions are \(\theta = 90^\circ\) or \(\theta = 131.8^\circ\).