Mathematics

Problem

The slopes

m_{1}

and

m_{2}

of the two tangents drawn from an external point

P

to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

are found to be the roots of the quadratic equation

m^{2} - 4m + 1 = 0

. Find the angle between these tangents.