SOLUTION: find the exact value of sin(arctan(3/4)-2arcsin(2/3)). I managed to get to sin(-7sqrt(5)/5) and i am stuck on what to do after that.

Draw the graphs of 1st quadrant angles  and 

Let  and 

The first right triangle will have  in standard position,
horizontal leg = 4, vertical leg = 3, and by the Pythagorean 
theorem hypotenuse = 

The second right triangle will have  in standard position,
vertical leg = 2, hypotenuse = 3, and by the Pythagorean 
theorem horizontal leg = .









Edwin