Solve: $2\cos^2\theta + 3\sin\theta - 3 = 0$, $\theta$ acute. $\theta = ?$

Replacing $\cos^2\theta$ with $1-\sin^2\theta$ gives $2\sin^2\theta-3\sin\theta+1=0$, which factors as $(2\sin\theta-1)(\sin\theta-1)=0$. The acute solution comes from $\sin\theta=\tfrac12$, giving $\theta=30^\circ$.