The Wronskian & Variation of Parameters · Superchallenge problem

Let $y$ solve $y''+2y'+2y=e^{-t}\sec t$ on $0\le t<\dfrac{\pi}{2}$ with $y(0)=0$, $y'(0)=0$. Find $\displaystyle\lim_{t\to\pi/2^-}y(t)$.