C_d=\frac{3}{\sqrt{\pi}}\frac{\Gamma\left(\frac{d+2}{2}\right)}{\Gamma\left(\frac{d+1}{2}\right)}\int_0^{\pi/3}\sin^d\theta d\theta | C_d=\frac{3}{\sqrt{\pi}}\frac{\Gamma\left(\frac{d+2}{2}\right)}{\Gamma\left(\frac{d+1}{2}\right)}\int_0^{\pi/3}\sin^d\theta d\theta |