Parametric differentiation

If the angle made by the tangent at the point $(x_0,y_0)$ on the curve $x=12(t+\sin t\cos t)$, $y=12(1+\sin t)^2$, $0<t<\dfrac\pi2$, with the positive $x$-axis is $\dfrac\pi3$, then $y_0$ is equal to:

Let $x(t)=2\sqrt2\cos t\sqrt{\sin2t}$ and $y(t)=2\sqrt2\sin t\sqrt{\sin2t}$, $t\in\left(0,\dfrac\pi2\right)$. Then $\dfrac{1+\left(\frac{dy}{dx}\right)^2}{\frac{d^2y}{dx^2}}$ at $t=\dfrac\pi4$ is equal to :

If the tangent at a point P, with parameter t, on the curve $x=4t^2+3$, $y=8t^3-1$, $t\in\mathbb R$, meets the curve again at a point Q, then the coordinates of Q are :

The distance, from the origin, of the normal to the curve, $x=2\cos t+2t\sin t$, $y=2\sin t-2t\cos t$ at $t=\dfrac\pi4$, is :

For the curve $y=3\sin\theta\cos\theta$, $x=e^\theta\sin\theta$, $0\le\theta\le\pi$, the tangent is parallel to $x$-axis when $\theta$ is :