How to integrate $\int_0^{\pi/2}\frac{1}{\sin^2(x)-\sin(x)\cos(x)+\cos^2(x)}\,\mathrm{d}x$ I got stuck at this definite integral, any idea?
$$\int_0^{\pi/2}\frac{1}{\sin^2(x)-\sin(x)\cos(x)+\cos^2(x)}\,\mathrm{d}x$$
Thank you.

\begin{aligned}
\int_{0}^{\frac{\pi}{2}} \frac{1}{\sin ^{2} x-\sin x \cos x+\cos ^{2} x} d x =& \int_{0}^{\frac{\pi}{2}} \frac{\sec ^{2} x}{\tan ^{2} x-\tan x+1} d x \\
=& \int_{0}^{\infty} \frac{d t}{t^{2}-t+1}, \text { where } t=\tan x \\
=& \int_{0}^{\infty} \frac{d t}{\left(t-\frac{1}{2}\right)^{2}+\frac{3}{4}} \\
=& \frac{2}{\sqrt{3}}\left[\tan ^{-1}\left(\frac{t-\frac{1}{2}}{\frac{\sqrt{3}}{2}}\right)\right]_{0}^{\infty} \\
=& \frac{2 \pi}{\sqrt{3}}
\end{aligned}
