AMC 10 2022a Problem 1

What is the value of $$3 + \frac{1}{3+\frac{1}{3+\frac{1}{3}}}?$$ $\textbf{(A) } \frac{31}{10} \textbf{(B) } \frac{49}{15} \textbf{(C) } \frac{33}{10} \textbf{(D) } \frac{109}{33} \textbf{(E) } \frac{15}{4}$