@LNZ You need to consult a legal/tax professional who can actually read the trust document.
If the property received a stepped-up basis in 2002, the property was not included in your mother's gross estate when she passed (i.e., she was perhaps solely an trustee/income beneficiary), and the property was rented by the trust since 2002 (when your father passed), then the fair market value on the date of death of your father would be basis for depreciation.
If the property continued being a rental from 2002 until 2015 and then was distributed to you and your brother from the trust, you would typically take a carryover basis from the trust including prior depreciation deductions taken by the trust.
Again, a scenario such as the one presented calls for review by a professional who can inspect the relevant documents. However, the basis for depreciation would not necessarily be the date you "inherited" the property nor the date the names of you and your brother were placed on the deed (which would obviously affect the date from which you and your brother would be responsible in terms of depreciation "recapture").
Finally, the Legal Information Institute is a project funded by the Cornell Law School (Cornell University) and, among other things, they publish the Constitution, law (including the Internal Revenue Code), and federal regulations (including Treasury Regulations) all of which are legal authority and which the IRS must follow.
