The nature of the vortex lattice melting transition in high-quality single crystals of Bi2Sr2CaCu2O8+delta has been studied by means of both in-plane and out-of-plane resistivity measurement in Corbino geometry and local ac-magnetic response measurement by using miniature coils. The vortex matter phase diagram has been established for the whole angular range, in particular, focusing in detail on angles within a few degrees of the ab-plane. The first-order vortex melting phase transition has been clearly observed in magnetic fields tilted away from the c-axis, indicating the crossing lattice structures. However, at about +/- 0.2degrees from the ab-plane, a distinct anomaly was found, suggesting a two-stage melting phase transition in parallel magnetic fields: the vortex-lattice --> smectic --> liquid phase transition, or transitions from the crossing vortex-lattice to the tilted vortex-lattice near the ab-plane. Another anomaly, in the temperature dependence of resistance in parallel magnetic fields, indicated the revival of the first-order nature of the transition very close to T.