Question: What county is the higher education institution of Newington College Headmaster Joseph Coates located in ?

text: Newington College
College staff -- Presidents and headmasters

Newington College is a multi-campus independent Uniting Church single-sex and co-educational early learning, primary and secondary day and boarding school for boys, located in Stanmore, an inner-western suburb of Sydney, New South Wales, Australia. Established in 1863 at Newington House, Silverwater, the College celebrated its sesquicentenary in 2013. The college is open to boys of all faiths and denominations. Newington has been governed by an Act of Parliament since 1922. Newington has two preparatory schools, Wyvern House, in Cambridge Street, Stanmore, and a school at Lindfield, on Sydney's Upper North Shore. Newington currently caters for approximately 2,000 students from Year K to Year 12. Edmund Webb House, a boarding facility, is in Cambridge Street, Stanmore. The Robert Glasson Memorial Boat Shed is on the Parramatta River at Abbotsford and contains a boarding facility for thirty boys. The College is a member of the Association of Heads of Independent Schools of Australia (AHISA), the Junior School Heads Association of Australia (JSHAA), the Australian Boarding Schools' Association, and a founding member of the Athletic Association of the Great Public Schools of New South Wales (AAGPS). The College prepares students for the International Baccalaureate Diploma Programme and the NSW Higher School Certificate.
Headmaster Education Previous positions held
Rev . James Egan Moulton 1863 Kingswood School Founding Headmaster , Tupou College , Tonga
George Metcalfe 1867 - 1869 University of Melbourne University of Sydney Proprietor and Headmaster , High School , Goulburn Founding Headmaster , Druitt Town Public School
Michael Howe 1868 - 1877 Trinity College , Dublin University of Melbourne Founding Headmaster , Galt Grammar School Headmaster , Jarvis Collegiate Institute , Toronto
Joseph Coates 1877 - 1883 Huddersfield College Founding Headmaster , Sydney Boys ' High School
William Williams 1884 - 1992 Newark Grammar School Trinity College , Cambridge Professor of Classics & English Literature , University of Tasmania
Arthur Lucas 1893 - 1898 Kingswood School Balliol College , Oxford Headmaster , Sydney Grammar School Professor of Mathematics , University of Tasmania
Edward William Cornwall 1899 Keble College , Oxford Acting Headmaster , Ipswich Grammar School Lecturer Classics and Languages , University of Melbourne
Rev . Charles Prescott 1900 - 1931 Kingswood School Worcester College , Oxford Founding Headmaster , Wesleyan Ladies ' College , Sydney
Philip Le Couteur 1931 - 1948 Queen 's College , Melbourne University College , Oxford University of Bonn , Germany Headmaster , Methodist Ladies ' College , Melbourne Headmaster , Hale School , Perth
Mervyn Austin 1950 - 1951 Melbourne Grammar School University of Melbourne Christ Church , Oxford Professor of Classics and Ancient History , University of Western Australia
Lawrence Pyke 1952 - 1960 Wesley College , Melbourne University of Melbourne University of Oxford Dean of Graduate Studies , University of Melbourne
Ernest Duncan 1962 University of Otago Columbia University Professor of Mathematics , Rutgers University
Rev . Douglas Trathen 1963 - 1970 Canterbury Boys ' High School University of Sydney Headmaster , Wolaroi College , Orange
Tony Rae 1972 - 1993 The Scots College , Sydney University of Sydney Headmaster , Albury Grammar School
Michael Smee 1993 - 2003 The King 's School , Sydney University of Sydney Headmaster , Pulteney Grammar School , Adelaide
David Scott 2003 - 2009 University of Western Australia Murdoch University Edith Cowan University Headmaster , Kingswood College , Melbourne Headmaster , Anglican Church Grammar School , Brisbane
David Mulford 2009 - 2018  Principal , Radford College , Canberra Headmaster , Blue Mountains Grammar School
Michael Parker 2019 - incumbent James Ruse Agricultural High School University of Sydney Headmaster , Oxley College , Bowral Deputy Headmaster , Cranbrook School , Sydney