  Polarized dust emission is widely used to trace the plane-of-the-sky (POS)
component of interstellar magnetic fields in two dimensions. Its potential to
access three-dimensional magnetic fields, including the inclination angle of
the magnetic fields relative to the line-of-sight (LOS), is crucial for a
variety of astrophysical problems. Based on the statistical features of
observed polarization fraction and POS Alfv\'en Mach number $\overline{M_{\rm
A}}_{,\bot}$ distribution, we present a new method for estimating the
inclination angle. The magnetic field fluctuations raised by anisotropic
magnetohydrodynamic (MHD) turbulence are taken into account in our method. By
using synthetic dust emission generated from 3D compressible MHD turbulence
simulations, we show that the fluctuations are preferentially perpendicular to
the mean magnetic field. We find the inclination angle is the major agent for
depolarization, while fluctuations of magnetic field strength and density have
an insignificant contribution. We propose and demonstrate that the mean
inclination angle over a region of interest can be calculated from the
polarization fraction in a strongly magnetized reference position, where
$\overline{M_{\rm A}}_{,\bot}^2\ll1$. We test and show that the new method can
trace the 3D magnetic fields in sub-Alfv\'enic, trans-Alfv\'enic, and
moderately super-Alfv\'enic conditions ($0.4\lesssim M_{\rm A}\lesssim1.2$). We
numerically quantify that the difference between the estimated inclination
angle and actual inclination angle ranges from 0 to $20^\circ$ with a median
value of $\le10^\circ$.
