Answer
a. $ \phi=63.4^{\circ} $
b. $ \phi=71.6^{\circ} $.
Work Step by Step
The first polarizer filters out half the incident unpolarized light.
$$I_1=\frac{1}{2}I_o$$
The fraction filtered out by the second polarizer depends on the angle between the axes of the two polarizers. At the end:
$$I_2=I_1cos^2\phi=\frac{1}{2}I_o cos^2 \phi=0.100I_0 $$
$$ cos \phi=\sqrt{2/10} $$
$$ \phi=63.4^{\circ} $$
b. Now the first filter passes all of the incident light.
$$I_1=I_o$$
The fraction filtered out by the second polarizer depends on the angle between the axes of the two polarizers. At the end:
$$I_2=I_1cos^2\phi=I_o cos^2 \phi=0.100I_0 $$
$$ cos \phi=\sqrt{1/10} $$
$$ \phi=71.6^{\circ} $$