single classed arcane heirophant-a build idea

so...the wild defender ranger is a ranger who gets trackless step at 3rd level, among other things, while others are replaced. now, if I take sword of the arcane order, it means my ranger is both an arcane spellcaster and a divine spellcaster.
now here is my question-can I, by RAW, take the arcane heirophant prc and advancing my ranger casting both as arcane and as divine, thus using a theurge class to advance my casting...both as divine and as arcane? I dont really see a *HUGE* optimization potential, but I just want to know if it is possible...
any thoughts?

Actually, taking SotAO means you're a divine caster that can prepare wizard spells in your divine spell slots. The feat doesn't say you become an arcane caster, but the ranger or paladin does say you're a divine caster.

So no you couldn't take a theurge class and double dip the caster advancement.