\begin{questions}
\item $\begin{aligned}[t]
\cos\frac{2\pi}{3} + \sin\frac{\pi}{6} & = -\cos\frac{\pi}{3}+ \sin\frac{\pi}{6}\\
& = -\frac{1}{2}+\frac{1}{2}\\
& = 0.
\end{aligned}$

\item $\begin{aligned}[t]
\sin\frac{3\pi}{4} + \sin\frac{5\pi}{4} & = \sin\frac{\pi}{4} + \sin\left(-\frac{3\pi}{4}\right)\\
& = \sin\frac{\pi}{4} - \sin\frac{\pi}{4}\\
& = 0.
\end{aligned}$

\item $\begin{aligned}[t]
1+\sin^2\frac{\pi}{4}+\cos^2\frac{3\pi}{4} & = 1 + \sin^2\frac{\pi}{4} + \left(-\cos\frac{\pi}{4}\right)^2\\
& = 1 + \underbrace{\sin^2\frac{\pi}{4} + \cos^2\frac{\pi}{4}}_{=1}\\
& = 2.
\end{aligned}$
\end{questions}
