How to calculate the tangent angle with the axis of an ellipse I hava an ellipse. I know its' equation.

For a given 't' how can I calculate angle "alpha". (I also know the coordinate of the tangent point)

The tangent is in the direction of 
$$\left(\frac{\mathrm{d}x}{\mathrm{d}t},\frac{\mathrm{d}y}{\mathrm{d}t}\right)$$
Then the slope of the tangent is given by
$$\frac{\frac{\mathrm{d}y}{\mathrm{d}t}}{\frac{\mathrm{d}x}{\mathrm{d}t}}=\frac{10\cos{t}}{-30\sin{t}}=-\frac{1}{3}\cot{t}$$
The angle is the $\arctan$ of the slope
