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The factor of four and why Goldman has a different factor is explained on page 880 of Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces.
A derivation with prefactor four is given in section 2 of The complex symplectic geometry of the deformation space of complex projective structures.

The factor of four and why Goldman has a different factor is explained on page 6 of Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces.
A derivation with prefactor four is given in section 2 of The complex symplectic geometry of the deformation space of complex projective structures.

The factor of 4 and why Goldman has a different factor is explained on page 880 of Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces.
A derivation with the factor of 4 is given in section 2 of The complex symplectic geometry of the deformation space of complex projective structures.

The factor of four and why Goldman has a different factor is explained on page 880 of Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces.
A derivation with prefactor four is given in section 2 of The complex symplectic geometry of the deformation space of complex projective structures.

The factor of 4 and why Goldman has a different factor is explained on page 880 of Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces.

The factor of 4 and why Goldman has a different factor is explained on page 880 of Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces.
A derivation with the factor of 4 is given in section 2 of The complex symplectic geometry of the deformation space of complex projective structures.