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What is a reasonable date for the fiscal year?"
A fiscal year begins on the date of death in the case of an estate and the date the trust becomes irrevocable in the case of a trust (which is also generally the date of death with respect to a grantor (revocable) trust).
For example, if the fiscal year began on 4/3/18, it would end on 3/31/19 and the income tax return, if required, would be due by 7/15/19 (which is the 15th day of the 4th month following the close of the tax year).
See https://www.irs.gov/instructions/i1041#idm140630132069712
