  We theoretically study the angular displacements estimation based on a
modified Mach-Zehnder interferometer (MZI), in which two optical parametric
amplifiers (PAs) are introduced into two arms of the standard MZI,
respectively. The employment of PAs can both squeeze the shot noise and amplify
the photon number inside the interferometer. When the unknown angular
displacements are introduced to both arms, we derive the multiparameter quantum
Cram\'er-Rao bound (QCRB) using the quantum Fisher information matrix approach,
and the bound of angular displacements difference between the two arms is
compared with the sensitivity of angular displacement using the intensity
detection. On the other hand, in the case where the unknown angular
displacement is in only one arm, we give the sensitivity of angular
displacement using the method of homodyne detection. It can surpass the
standard quantum limit (SQL) and approach the single parameter QCRB. Finally,
the effect of photon losses on sensitivity is discussed.
