What is the sum of all possible values of $t$ between $0^{\circ}$ and $360^{\circ}$ such that the triangle in the coordinate plane whose vertices are $(\cos 40^{\circ}, \sin 40^{\circ}),(\cos 60^{\circ}, \sin 60^{\circ}) \text {, and }(\cos t^{\circ}, \sin t^{\circ})$ is isosceles?