Blu-ray uses frame packed 3D as the standard format which was introduced after your projector was released. Your projector may work with certain computers which put out side-by-side or top-bottom 3D, but that's not how the Playstation units do it.
Page 70 of the manual also indicates that 3D is ONLY supported on the PC input, with no compatibility at all on the HDMI input.https://www.projectorcentral.com/pdf/projector_manual_5859.pdf
So, if you want the very good 3D which projectors can deliver, you will need a model which supports frame-packed 3D from a blu-ray disc player. Many current generation 1080p projectors, starting at about $500, can do this.
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