Is it possible to retrieve sum of square, df, F value and P value after using linear mixed model?

Question

I have complete randomized block design with 3 treatment levels (control, moderate, heavy thinning in forest) and 3 replicates for each treatments. I collected rainfall under the canopy called as Throughfall(response variable). It was collected by monthly and study conducted 3 years. we considered treatment and month as fixed, year and replicates as random effects. So I have in my spreadsheet 324 cells total (12 month* 3 trt* 3 rep * 3 year). I just would like to have an anova table including SS, df, F value and P value for both fixed and random effects. here below that is only for fixed effect and I would like to report random effects and interactions too. I could not find the code which I can apply. Also how can I apply pairwise comparison? So can anyone help me about that? Thank you,

I run the code below:

library(MASS)
library(dplyr)
library(lme4)
library(Matrix)

test<-lmer( log ~ trt + as.factor(month) +trt*as.factor(month)+ (1| year )+ (1|rep)  , data=dataf,REML="TRUE")
AIC(test)
summary(test)
anova(test)


######results####

Linear mixed model fit by REML ['lmerMod']
Formula: log ~ trt + as.factor(month) + trt * as.factor(month) + (1 | year) + (1 | rep2)
   Data: dataf

REML criterion at convergence: 885.6

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.9667 -0.7787  0.1229  0.6077  2.5410 

Random effects:
 Groups   Name        Variance Std.Dev.
 year     (Intercept) 0.009945 0.09973 
 rep2     (Intercept) 0.000000 0.00000 
 Residual             0.957992 0.97877 
Number of obs: 324, groups:  year, 3; rep2, 3

> anova(test)
Analysis of Variance Table
                     npar  Sum Sq Mean Sq F value
trt                     2   0.656  0.3282  0.3426
as.factor(month)       11 203.506 18.5006 19.3118
trt:as.factor(month)   22   0.270  0.0123  0.0128

I applied linear mixed model for my study, I would expect to have anova table.