$$
theta=60.0text{textdegree}
$$

Unknown:

$$
I_{f}/I_{i}
$$

Solution

$$
frac{I_{f}}{I_{i}}=frac{1}{2}cos^{2}theta=frac{1}{2}timescos^{2}60.0text{textdegree}=frac{1}{8}
$$

So the final intensity will be $1/8$ times the initial intensity.
Hence the transmitted intensity will decrease.

$$
I_{f}=0.250I_{i}Rightarrow I_{f}/I_{i}=0.250
$$

Unknown:

$$
theta=?
$$

Solution

$$
cos^{2}theta=2frac{I_{f}}{I_{i}}=2times0.250=0.500=frac{1}{2}
$$

$$
thereforetheta=cos^{-1}left(frac{1}{sqrt{2}}right)=45text{textdegree}
$$

$$
theta=30.0text{textdegree}
$$

Unknown

$I_{f}/I_{i}=?$

We know that

$$
frac{I_{f}}{I_{i}}=frac{1}{2}cos^{2}theta=frac{1}{2}cos^{2}30.0text{textdegree}=0.375
$$

So $0.375$ fraction of the initial intensity will be transmitted.

$$
I_{i}=1.2 {rm W/m^{2}}
$$

$$
theta_{1}=35text{textdegree}
$$

$$
theta_{2}=45text{textdegree}
$$

Known

$I_{f}=?$

Solution:

$$
I_{f}=I_{i}cos^2theta_{1}cos^2theta_{2}=left(1.2 {rm W/m^{2}}right)left(cos^2 35text{textdegree}right)left(cos^2 45text{textdegree}right)=0.40 {rm W/m^{2}}
$$