There is no indication on the Indian calender that any festivals that took place on June 10, 1987. It does however indicate that on June 9, 1987 Vaikasi Vishaka took place.
You can get calendar for June 1987 at calendarlabs.com
The Silent Majority - 1987 was released on: USA: 18 June 1987 (Chicago International Film Festival)
Pure Country - 1987 TV was released on: USA: 4 June 1987 (Silver Lake Film Festival)
Indian Girl - 2010 was released on: USA: 11 June 2010 (deadCENTER Film Festival) (premiere)
A calendar for June 1947 can be found below this answer.
Le jupon rouge - 1987 was released on: France: 17 June 1987 Canada: 13 September 1987 (Toronto Film Festival) USA: 21 March 1988 (New York New Directors and New Films Festival)
A Feast of Fools - 1987 was released on: USA: 15 May 1987 (Chicago, Illinois) USA: 22 May 1987 (Illinois Film and Video Festival) Italy: 23 October 1987 (Turin Film Festival) USA: 10 June 1988 (TV premiere)
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Nanou - 1986 was released on: Canada: 7 September 1986 (Toronto Film Festival) UK: 27 February 1987 France: 17 June 1987 USA: 28 September 1988 (New York Film Festival) West Germany: 29 June 1989
Vzlomshchik - 1987 was released on: Italy: September 1987 (Venice Film Festival) Hungary: 4 February 1988 USA: 17 August 1988 (New York City, New York) Russia: 24 June 2003 (Moscow Film Festival)
See the related link for a full calendar of June 1946.
A calendar for June 1944 can be found in the external link beneath this question.