Sorry, but I'm not too sure what you want us to do here. Are we going to graph this? Find the intercepts? Find the zeros? Something else?
I would assume we are graphing it. To graph it, I would use a calculator. Be careful. The arcsin for this would be sin-1. the second function of the sin button. To access it, you would press the "2nd" button then the sin button.
So, to graph this, on a graphing calculator, you would press "Y=". You will see Y1=, Y2=, Y3=, etc., on the left side. Clear all other equations out. Then, on the first line, I would input the function. It would look something like:
Y1= = (sin-1(x))2-2x+2*(√(1-x2))*sin-1(x)
But, make sure you change your calculator to radians. Assuming a TI 83 Graphing Calculator, press "MODE". Then, highlight "RADIAN" on the third line down. Press "enter". Then, press graph. You will see a very small graph right around the origin. You would need to zoom in. You would press "ZOOM", then press 2, then press "enter". You will see the graph zoom in.
Good luck, djshan. I hope this helps.