Mathematics

Problem

Solve the equation

\cos\bigl(2\theta + 45^{\circ}\bigr)= -\dfrac{\sqrt{2}}{2}

, where

\theta

is measured in degrees. a. (i) Obtain the general solution for

\theta

. b. (ii) Write all values of

\theta

that satisfy the equation in the interval

-180^{\circ} \le \theta < 180^{\circ}