Molecule MX3 has zero dipole moment because it has a trigonal planar molecular geometry with no lone pairs on the central atom. The sigma bonding orbitals used by M are sp2-hybridized.

Trigonal Planar Molecular Geometry
The molecule MX3 has a trigonal planar molecular geometry because it has three bonding groups and no lone pairs on the central atom. This geometry is achieved when the central atom forms three sigma bonds with three surrounding atoms, and these bonds are arranged in a flat, triangular shape around the central atom.

Zero Dipole Moment
A molecule has a dipole moment if there is a separation of positive and negative charges within the molecule. This separation of charges creates a dipole moment vector. In the case of MX3, the molecule has a trigonal planar geometry, which means that the bond dipoles cancel each other out due to their symmetric arrangement. As a result, the molecule has no net dipole moment and is considered nonpolar.

Sigma Bonding Orbitals
In MX3, the central atom M forms three sigma bonds with three surrounding atoms, X. These sigma bonds are formed by overlapping hybrid orbitals on M with the atomic orbitals on X. The type of hybrid orbitals used by M can be determined by examining the electron configuration and the number of sigma bonds formed.

sp2-Hybridized Orbitals
In the case of MX3, the central atom M has an atomic number of 21. The electron configuration of M is 1s2 2s2 2p6 3s2 3p6 4s2 3d5. The valence shell electron configuration of M is 3s2 3p6 3d5. To achieve a trigonal planar geometry, the central atom M must hybridize its valence orbitals.

The process of hybridization involves mixing of atomic orbitals to form new hybrid orbitals that are suitable for bonding. In the case of MX3, the central atom M undergoes sp2 hybridization, which means that three valence orbitals of M (one 3s orbital and two 3p orbitals) are combined to form three sp2 hybrid orbitals.

These sp2 hybrid orbitals are then used to form sigma bonds with the three surrounding atoms X. The remaining unhybridized 3p orbital on M may contain lone pairs or participate in pi bonding, but it does not contribute to the molecular geometry or the dipole moment of MX3.

In conclusion, the sigma bonding orbitals used by the central atom M in molecule MX3 are sp2-hybridized. This hybridization allows the central atom to form three sigma bonds in a trigonal planar molecular geometry, resulting in a molecule with zero dipole moment.