A uniform beam (EI = constant) PQ in the form of a quarter-circle of radius R is fixed at end P and free at the end Q, where a load W is applied as shown. The vertical downward displacement, \(\delta_q\), at the loaded point Q is given by: \(\delta_q = \beta(\frac{WR^3}{EI})\) Find the value of \(\beta\) (correct to 4-decimal places).