Just briefly looked at part (b) and you solve it like a normal trig equation.
Sin2θ=1/4 for 0<θ<360.
Change the domain to suit the equation i.e. 0<2θ<720. Now solve the equation within this domain.
sin2θ=1/4 for 0<2θ<720
2θ=14 , 166 , 374, 526 (to the nearest degree)
θ = 7, 83, 187...