\[\frac{1}{{3 + \frac{1}{{\frac{3}{2} + \frac{1}{{\frac{3}{3} + \frac{1}{{\frac{3}{4} + \frac{1}{{\frac{3}{5} + \frac{1}{{...}}}}}}}}}}}} = 5 - \frac{{3\pi }}{2}\]