Finding the angle between two tangents of a curve I just got back from my math test. In the test I encountered the following question:

A curve is defined by the equation $$x^3+y^3=3xy$$ Find the angle between the tangents at points (-1,1) and (1,2).

After differentiating implicitly, we get:
$\frac{dy}{dx} = \frac{y-x^2}{y^2-x}$
And the equation of the tangents at the above points are:
$y = \frac{x}{3} + \frac{5}{3}$ and $y = 1$
So, I formed a triangle representing one part of the intersection between the two lines, which looks something like this. 
Therefore, the angle between them would be $$\arcsin(4/5)$$ Is my approach right or wrong? If its wrong then how would we do this question?

No, it should be $\arctan\frac{1}{3}.$
By the way, your calculations of slopes are right.
