Story highlights Baldwin says Costner, others tricked him into selling stock just before its value would rise

BP placed $52 million order for oil separators 4 days after Baldwin committed to selling his stock

Costner's company developed the machines to separate spilled oil from water in the 1990s

Both actors must attend each day of the federal trial

Lawyers for Kevin Costner and Stephen Baldwin began choosing jurors Monday to decide a legal dispute between the two actors stemming from the 2010 Gulf oil spill.

Baldwin and a New Orleans businessman say Costner and others tricked them into selling their stock in a company that made oil spill cleanup machines the same week BP placed a $52 million order for the technology.

The judge has ordered both actors to attend each day of the trial, which is being heard in a federal court in New Orleans.

The oil separation technology was developed in the 1990s by a company created by Costner , but Baldwin became involved while in New Orleans to produce a documentary about the Deepwater Horizon spill in the Gulf of Mexico in May 2010.

Baldwin and Spyridon Contogouris decided to sell their stock soon after getting it because of differences with other shareholders, according to the lawsuit. They signed an agreement to sell their shares to Patrick Smith, who then transferred them to a company partly owned by Costner, on June 11, 2010.

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BP announced on June 15, 2010, it would lease 32 machines from the company.

If Smith and Costner had told them BP was placing a huge order, they would not have sold, the suit said. The 10% of the company that Baldwin sold for $500,000 should have been worth $3.8 million, while the 28% stake sold by Contogouris for $1.4 million was worth $10.6 million, the suit said.

Lawyers for Costner and Smith contend Baldwin and Contogouris sold their stock "with eyes wide open, to get out of a soured business relationship and to invest in other ventures."

They knew that BP might place the order, a defense filing said. It was widely reported in the news and Costner testified about it to Congress two days before the stock sale.

Contrary to trying to trick Baldwin into selling his shares, Costner was "dumbfounded," "flabbergasted" and "furious" when he learned Baldwin and Contogouris had sold out "because it enabled plaintiffs to cash out their interests" before the company had earned any money, the defense filing said.

Costner and Baldwin are both on the list of witnesses expected to testify.