Chapter 5.4, Problem 34E

Find the function of the form $f\left(t\right)=c_0+c_1\sin \left(t\right)+c_2\cos \left(t\right)+c_3\sin \left(2t\right)+c_4\cos \left(2t\right)$
that best fits the data points $\left(0,0\right),\left(0.5,0.5\right),\left(1,1\right),\left(1.5,1.5\right),\left(2,2\right),\left(2.5,2.5\right),\left(3,3\right)$ , using least squares.Sketch the solution, together with the function $g\left(t\right)=t$ .