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I'm completing my tutoring booklet for trigonometry and I have a question that is quite difficult. I've never done anything like it and my solutions page only has the final answer. I'd like to see how the result is found step-by-step, so if anyone can help me out or at least guide me to the solution it would be much appreciated.

http://speedcap.net/sharing/files/57/af/57afa49f650622a931c668f649477a83.png

http://speedcap.net/sharing/files/6a/e5/6ae5a228d615fb949ba020cd1a1c725d.png

If you cannot read the question, it is:

sin(x) = (√3)/2 in the circle with centre O, shown on the right. Furthermore AB // OP and m OA = 1 unit. What is the area of the shaded region?

Thanks in advance!