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Some 74% of Irish people want the proposed Transatlantic Trade and Investment Partnership (TTIP) and similar trade deals put to a referendum if they look likely to become law, according to a new Red C survey.
The US-EU free trade deal, which has been in the works for three years, has 69% of Irish adults worried.
Similarly, people also want a similar poll on Europe's planned trade agreement with Canada.
The Comprehensive Economic and Trade Agreement (CETA) between Canada and the EU has also taken years to negotiate, and could finally come into place in 2017.
People aged between 18 and 24 are the most sceptical of proposed trade agreements, and the group most in favour of the public deciding on whether or not they should be approved or rejected via referenda.
Uplift commissioned Red C to conduct the poll with a random sample of 1,004 adults across the country interviewed by telephone earlier in July.
The sentence hearing of three former bankers who conspired to mislead the public about Anglo Irish Bank is due to get underway today.
They were convicted last month following the longest criminal trial in the history of the State.
At just under 62 hours, the record for jury deliberations was also broken.
The end result was the convictions of former Anglo executives Willie McAteer and John Bowe and the former CEO of Irish Life and Permanent Denis Casey.
They were found to have knowingly facilitated €7.2bn in back-to-back transactions between March and September 2008 that made Anglo's corporate deposits look a lot healthier than they actually were.
In doing so, they conspired to mislead investors and depositors in the former bank.
Peter Fitzpatrick, who used to work as ILP's finance director, was acquitted of the same charge.
The others are all due back in court today for what's expected to be a lengthy sentence hearing.
Additional reporting: Court correspondent Frank Greaney.
Ryanair has reported profit growth of 4% for the first quarter of its financial year.
Profits after tax climbed to €256m. Basic earnings per share increased 12% to 20.01 cent.
Revenue for the three months to the end of June grew 2% when compared to the same period in 2015, from €1.65bn to €1.69bn.
The low fares airline carried 31.2 million passengers during its first quarter, up 11% on the same period last year.
CEO Michael O'Leary said that the company was maintaining its guidance that full year profits would rise by approximately 12%, while cautioning that the UK's Brexit decision would pose significant risks for the rest of 2016.
British Prime Minister Theresa May has moved to reassure Northern Ireland that its best interests will be taken into account as the UK negotiates a Brexit.
She said she wants to fully engage with Stormont ministers preparing for negotiations on the UK's exit from the European Union, as she heads to Belfast today.
May, who is travelling to Northern Ireland for the first time since becoming PM, is due to meet First Minister Arlene Foster and Deputy First Minister Martin McGuinness at Stormont.
"I am delighted to be visiting Northern Ireland," May said. "I made clear when I became Prime Minister that I place particular value on the precious bonds between the nations of the United Kingdom.
"I want to assure the people of Northern Ireland that I will lead a government which works for everyone across all parts of the United Kingdom, and that Northern Ireland is a special and valued part of that union."
In the EU referendum last month, Northern Ireland voted to stay in by 56% to 44%.
May said Brexit talks must take into account Northern Ireland's land border with the Republic of Ireland and Europe, and the potential disruption to the free movement of people and goods.