The question is as follows:
Parameterize the intersection of the cylinder $x^2 + y^2 = 1$ and the plane $x+y+z = 1$ in $\mathbb{R}^3$ and find its arclength.
I have come as far as parameterizing each variable as a function of $t$, such that
$$x(t) = \sin(t) \qquad y(t) = \cos(t) \qquad z(t) = 1 - \sin(t) - \cos(t)$$
and have reached the expression
$$\begin{align} s &= \int_{0}^{2\pi}{\sqrt{(x'(t))^2 + (y'(t))^2 + (z'(t))^2} dt} \\ &= \int_{0}^{2\pi}{\sqrt{2-2\cos(t)\sin(t)}dt} \end{align}$$
I have no clue as to how to proceed from here. I have just started learning multivariable calculus, so I'm not too familiar with special integral identities. Should I just run it through a calculator and get an approximated value? Any help would be appreciated.