An object is moving in the plane according to these parametric equations:

x(t) = πt + cos(4πt + π/2)
y(t) = sin(4πt + π/2)

the slope of the tangent line to the path at time t is

4πcos(4πt + π/2) divided by (π-4πsin(4πt+π/2))

the first time the tangent line is vertical will be t = ?

the second time the tangent line is vertical will be t = ?