Cardiff Crown Court in south Wales heard that toddler Elsi Scully-Hicks died in May 2016 after suffering a fractured skull while being violently shaken, two weeks after being formally adopted by defendant Matthew Scully-Hicks and his husband.
The toddler sustained bruises, a broken leg and fell down a flight of stairs during the eight months that she was in the care of the 31-year-old fitness instructor.
Scully-Hicks told the court that he was unable to handle the pressures of bringing up the child, calling her "a psycho" and "Satan dressed up in a Babygro" in text messages.
Jurors unanimously found him guilty of murder following a four-week trial.
Prosecutor Paul Lewis said the attack "required considerable force in gripping of the child because of the medical evidence of the fractures of the wrist. There must have been forceful shaking.
"There must have been gripping and shaking. Either her head was hit against a hard surface, or a hard object was used to strike Elsie to the head," he added.
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