$$\begin{aligned} & \frac{d y}{d x}+3\left(\tan ^2 x\right) y+3 y=\sec ^2 x \\ & \Rightarrow \frac{d y}{d x}+3 \sec ^2 x y=\sec ^2 x \\ & \text { I.F }=e^{\int 3 \sec ^2 x d x} \\ & \quad=e^{3 \tan x} \end{aligned}$$

$$\begin{aligned} & y \cdot e^{\tan x}=\int e^{3 \tan x} \cdot \sec ^2 x d x+c \\ & y \cdot e^{3 \tan x}=\frac{e^{3 \tan x}}{3}+c \\ & \text { Also } f(0)=\frac{1}{3}+e^3 \\ & \Rightarrow\left(\frac{1}{3}+e^3\right)=\frac{1}{3}+c \\ & \Rightarrow c=e^3 \\ & \therefore y \cdot e^{3 \tan x}=\frac{e^{3 \tan x}}{3}+e^3 \\ & \text { Put } x=\frac{\pi}{4} \end{aligned}$$

$y e^3=\frac{e^3}{3}+e^3 \Rightarrow y=\frac{4}{3}$