A knife-wielding mentally-ill young woman who was shot dead by police outside a western Sydney Hungry Jack's had been using the tip of the blade to brush hair away from her face, her inquest has heard.

Courtney Topic was brandishing a large kitchen knife when she lunged at two officers in the fast-food restaurant's car park at West Hoxton in February 2015.

New South Wales Police tried to subdue the 22-year-old with pepper spray and a defective Taser before shooting her in the chest in broad daylight, and although they carried out CPR, she died shortly afterwards.

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Courtney Topic (pictured) was brandishing a large kitchen knife when she lunged at two officers in the fast-food restaurant's car park at West Hoxton in February 2015

Ms Topic's parents Leesa and Ron were in Glebe Coroner's Court on Monday, and her mother wept alongside other family members.

Counsel assisting Gerard Craddock SC told the court Ms Topic had suicidal thoughts and likely suffered undiagnosed schizophrenia when she died.

The Carnes Hill woman, who was just a few weeks shy of her 23rd birthday, was spotted swinging the 30cm knife backwards and forwards and talking to herself in the minutes leading up to her death.

An inquest into the death of the 22-year-old began in the NSW Coroner's Court in Glebe on Monday, and is expected to continue all week

Some witnesses saw her swaying and resting the flat of the blade on her head and pressing the weapon into her stomach while sipping from a takeaway cup.

An expert medical witness is expected to give evidence stating Ms Topic had likely developed an undiagnosed schizophrenia and was experiencing an untreated 'psychosis for a sustained period of time', Mr Craddock said.

The court heard Ms Topic had a major depressive disorder and ADHD (Attention deficit hyperactivity disorder), and was taking antidepressants at the time of her death on February 10.

NSW Police tried to subdue the 22-year-old with pepper spray and a defective Taser before shooting her in the chest in broad daylight, and although they carried out CPR, she died shortly afterwards

Police arrived on the scene after receiving several triple-zero calls before midday, and 41 seconds later a single fatal shot was fired.

The inquest will examine the adequacy of police training for responding to people suffering mental health problems, communication strategies and the use of weapons.

The court heard two of the three officers had only had one day of mental health training before the incident, and the third had none at all.

Police arrived on the scene after receiving several triple-zero calls before midday, and 41 seconds later a single fatal shot was fired

The court heard two of the three officers had only had one day of mental health training before the incident, and the third had none at all

Police and Forensic Service personnel on the scene of a shooting at a fast food restaurant at West Hoxton, New South Wales