Considering only the principal values of the inverse trigonometric functions, the value of
\( \dfrac{3}{2} \cos^{-1}\sqrt{\dfrac{2}{2+\pi^{2}}} + \dfrac{1}{4} \sin^{-1}\dfrac{2\sqrt{2}\,\pi}{2+\pi^{2}} + \tan^{-1}\dfrac{\sqrt{2}}{\pi} \) is ____________.
